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Journal articles on the topic 'Hyperbolicity theory'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Campana, Frédéric, Lionel Darondeau, and Erwan Rousseau. "Orbifold hyperbolicity." Compositio Mathematica 156, no. 8 (August 2020): 1664–98. http://dx.doi.org/10.1112/s0010437x20007265.

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AbstractWe define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of orbifold pairs of general type that do not admit any global jet differential, even if some of these examples satisfy the Green–Griffiths–Lang conjecture. This contrasts with an important result of Demailly (Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q. 7 (2011), 1165–1207) proving that compact varieties of general type always admit jet differentials. We illustrate the usefulness of the study of orbifold jets by establishing the hyperbolicity of some orbifold surfaces, that cannot be derived from the current techniques in Nevanlinna theory. We also conjecture that Demailly's theorem should hold for orbifold pairs with smooth boundary divisors under a certain natural multiplicity condition, and provide some evidence towards it.

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2

Gromov, M. "Kähler hyperbolicity and $L_2$-Hodge theory." Journal of Differential Geometry 33, no. 1 (1991): 263–92. http://dx.doi.org/10.4310/jdg/1214446039.

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3

Adams, Colin, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang, Kate O’Connor, Natalia Pacheco-Tallaj, and Yi Wang. "TG-Hyperbolicity of virtual links." Journal of Knot Theory and Its Ramifications 28, no. 12 (October 2019): 1950080. http://dx.doi.org/10.1142/s0218216519500809.

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We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.

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4

Portilla, Ana, José M. Rodríguez, José M. Sigarreta, and Eva Tourís. "Gromov Hyperbolicity in Directed Graphs." Symmetry 12, no. 1 (January 6, 2020): 105. http://dx.doi.org/10.3390/sym12010105.

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In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem has potential applications to the development of solutions for secure data transfer on the internet.

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5

Riaza, Ricardo, and Caren Tischendorf. "The hyperbolicity problem in electrical circuit theory." Mathematical Methods in the Applied Sciences 33, no. 17 (November 21, 2010): 2037–49. http://dx.doi.org/10.1002/mma.1312.

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6

Iwaki, E., S. O. Juriaans, and A. C. Souza Filho. "Hyperbolicity of semigroup algebras." Journal of Algebra 319, no. 12 (June 2008): 5000–5015. http://dx.doi.org/10.1016/j.jalgebra.2008.03.015.

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7

Stewart, Andrew L., and Paul J. Dellar. "Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear." Journal of Fluid Mechanics 723 (April 16, 2013): 289–317. http://dx.doi.org/10.1017/jfm.2013.121.

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AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.

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8

Boyde, Guy. "p-Hyperbolicity of homotopy groups via K-theory." Mathematische Zeitschrift 301, no. 1 (January 7, 2022): 977–1009. http://dx.doi.org/10.1007/s00209-021-02917-1.

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AbstractWe show that $$S^n \vee S^m$$ S n ∨ S m is $${\mathbb {Z}}/p^r$$ Z / p r -hyperbolic for all primes p and all $$r \in {\mathbb {Z}}^+$$ r ∈ Z + , provided $$n,m \ge 2$$ n , m ≥ 2 , and consequently that various spaces containing $$S^n \vee S^m$$ S n ∨ S m as a p-local retract are $${\mathbb {Z}}/p^r$$ Z / p r -hyperbolic. We then give a K-theory criterion for a suspension $$\Sigma X$$ Σ X to be p-hyperbolic, and use it to deduce that the suspension of a complex Grassmannian $$\Sigma Gr_{k,n}$$ Σ G r k , n is p-hyperbolic for all odd primes p when $$n \ge 3$$ n ≥ 3 and $$0<k<n$$ 0 < k < n . We obtain similar results for some related spaces.

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9

Barreira, Luis, and Claudia Valls. "Spectral theory for invertible cocycles under nonuniform hyperbolicity." São Paulo Journal of Mathematical Sciences 12, no. 1 (August 11, 2017): 6–17. http://dx.doi.org/10.1007/s40863-017-0070-z.

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10

Bermudo, Sergio, José M. Rodríguez, and José M. Sigarreta. "Computing the hyperbolicity constant." Computers & Mathematics with Applications 62, no. 12 (December 2011): 4592–95. http://dx.doi.org/10.1016/j.camwa.2011.10.041.

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11

Valanis, K. C. "A Global Damage Theory and the Hyperbolicity of the Wave Problem." Journal of Applied Mechanics 58, no. 2 (June 1, 1991): 311–16. http://dx.doi.org/10.1115/1.2897187.

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It is well known that wave equation in materials that suffer damage in the course of deformation loses it hyperbolicity when the damage process is described by a continuum damage theory of the local type. Here we develop a global (nonlocal) damage theory by (a) introducing a damage coordinate which is a spatial functional of the strain field in the material domain and (b) stipulating that the rate of evolution of damage is with respect to the damage coordinate. We then derive the axial wave equation for a thin rod and thereby demonstrate that, while the rod experiences softening, the wave speed is given in terms of the secant modulus and the wave equation retains its hyperbolicity. Various other phenomena, such as the onset of inhomogeneous damage in the presence of homogeneous deformation and the tendency of axial specimens under tension to fracture invariably at the center, are also explained.

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12

CHO, JINSEOK, and JUN MURAKAMI. "THE COMPLEX VOLUMES OF TWIST KNOTS VIA COLORED JONES POLYNOMIALS." Journal of Knot Theory and Its Ramifications 19, no. 11 (November 2010): 1401–21. http://dx.doi.org/10.1142/s0218216510008443.

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For a hyperbolic knot, an ideal triangulation of the knot complement corresponding to the colored Jones polynomial was introduced by Thurston. Considering this triangulation of a twist knot, we find a function which gives the hyperbolicity equations and the complex volume of the knot complement, using Zickert's theory of the extended Bloch group and the complex volume. We also consider a formal approximation of the colored Jones polynomial. Following Ohnuki's theory of 2-bridge knots, we define another function which comes from the approximation. We show that this function is essentially the same as the previous function, and therefore it also gives the same hyperbolicity equations and the complex volume. Finally we compare this result with our previous one which dealt with Yokota theory, and, as an application to Yokota theory, present a refined formula of the complex volumes for any twist knots.

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13

IWAKI, E., E. JESPERS, S. O. JURIAANS, and A. C. SOUZA FILHO. "HYPERBOLICITY OF SEMIGROUP ALGEBRAS II." Journal of Algebra and Its Applications 09, no. 06 (December 2010): 871–76. http://dx.doi.org/10.1142/s0219498810004270.

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In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki–Juriaans–Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a ℤ-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

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14

Yong, Wen-An. "Basic structures of hyperbolic relaxation systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 5 (October 2002): 1259–74. http://dx.doi.org/10.1017/s0308210500002109.

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This work is concerned with basic structural properties of first-order hyperbolic systems with source terms divided by a small parameter ε. We identify a relaxation criterion necessary for the solution sequences indexed with ε to have reasonable limits as ε goes to zero. This relaxation criterion is shown to imply hyperbolicity of the reduced systems governing the limits. Moreover, we introduce a so-called GC-stability theory and strengthen the hyperbolicity result. The latter shows that there are no linearly stable hyperbolic relaxation approximations for non-hyperbolic conservation laws.

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15

Yong, Wen-An. "Basic structures of hyperbolic relaxation systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 5 (October 2002): 1259–74. http://dx.doi.org/10.1017/s0308210502000616.

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This work is concerned with basic structural properties of first-order hyperbolic systems with source terms divided by a small parameter ε. We identify a relaxation criterion necessary for the solution sequences indexed with ε to have reasonable limits as ε goes to zero. This relaxation criterion is shown to imply hyperbolicity of the reduced systems governing the limits. Moreover, we introduce a so-called GC-stability theory and strengthen the hyperbolicity result. The latter shows that there are no linearly stable hyperbolic relaxation approximations for non-hyperbolic conservation laws.

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16

Pesin, Yakov, and Vaughn Climenhaga. "Open problems in the theory of non-uniform hyperbolicity." Discrete & Continuous Dynamical Systems - A 27, no. 2 (2010): 589–607. http://dx.doi.org/10.3934/dcds.2010.27.589.

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17

Lafont, Jean-François, and Ivonne J. Ortiz. "Relative hyperbolicity, classifying spaces, and lower algebraic K-theory." Topology 46, no. 6 (November 2007): 527–53. http://dx.doi.org/10.1016/j.top.2007.03.001.

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18

Boffi, V. C., and K. Aoki. "Nonlinear hyperbolicity in kinetic theory of a gas mixture." Il Nuovo Cimento D 10, no. 9 (September 1988): 1013–29. http://dx.doi.org/10.1007/bf02450202.

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19

Mahmoudi, M. G. "A Remark on Transfers and Hyperbolicity." Communications in Algebra 32, no. 12 (December 31, 2004): 4733–39. http://dx.doi.org/10.1081/agb-200036737.

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20

Buzzi, Jérôme, and Todd Fisher. "Entropic stability beyond partial hyperbolicity." Journal of Modern Dynamics 7, no. 4 (2013): 527–52. http://dx.doi.org/10.3934/jmd.2013.7.527.

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21

Bermudo, Sergio, Walter Carballosa, José Rodríguez, and José Sigarreta. "On the hyperbolicity of edge-chordal and path-chordal graphs." Filomat 30, no. 9 (2016): 2599–607. http://dx.doi.org/10.2298/fil1609599b.

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If X is a geodesic metric space and x1, x2, x3 ( X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is ?-hyperbolic (in the Gromov sense) if any side of T is contained in a ?-neighborhood of the union of the other two sides, for every geodesic triangle T in X. An important problem in the study of hyperbolic graphs is to relate the hyperbolicity with some classical properties in graph theory. In this paper we find a very close connection between hyperbolicity and chordality: we extend the classical definition of chordality in two ways, edge-chordality and path-chordality, in order to relate this propertywith Gromov hyperbolicity. In fact, we prove that every edge-chordal graph is hyperbolic and that every hyperbolic graph is path-chordal. Furthermore, we prove that every path-chordal cubic graph with small path-chordality constant is hyperbolic.

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22

Dey, Papri, and Daniel Plaumann. "Testing Hyperbolicity of Real Polynomials." Mathematics in Computer Science 14, no. 1 (January 16, 2020): 111–21. http://dx.doi.org/10.1007/s11786-019-00449-w.

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23

Cândido, Murilo R., and Jaume Llibre. "Stability of Periodic Orbits in the Averaging Theory: Applications to Lorenz and Thomas Differential Systems." International Journal of Bifurcation and Chaos 28, no. 03 (March 2018): 1830007. http://dx.doi.org/10.1142/s0218127418300070.

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We provide new results in studying a kind of stability of periodic orbits provided by the higher-order averaging theory. Then, we apply these results to determining the [Formula: see text]-hyperbolicity of some periodic orbits of the Lorenz and Thomas differential systems.

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24

Fabbri, Luca, and Manuel Tecchiolli. "Restrictions on torsion–spinor field theory." Modern Physics Letters A 34, no. 37 (December 6, 2019): 1950311. http://dx.doi.org/10.1142/s0217732319503115.

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Torsion propagation and torsion–spin coupling are studied in the perspective of the Velo–Zwanziger method of analysis; specifically, we write the most extensive dynamics of the torsion tensor and the most exhaustive coupling that is permitted between torsion and spinors, and check the compatibility with constraints and hyperbolicity and causality of field equations: we find that some components of torsion and many terms of the torsion–spin interaction will be restricted away and as a consequence, we will present the most general theory that is compatible with all restrictions.

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25

Diaz, L. J., and J. Rocha. "Heterodimensional cycles, partial hyperbolicity and limit dynamics." Fundamenta Mathematicae 174, no. 2 (2002): 127–86. http://dx.doi.org/10.4064/fm174-2-2.

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26

Brotbek, Damian. "Hyperbolicity related problems for complete intersection varieties." Compositio Mathematica 150, no. 3 (November 18, 2013): 369–95. http://dx.doi.org/10.1112/s0010437x13007458.

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AbstractIn this paper we examine different problems regarding complete intersection varieties of high multidegree in a smooth complex projective variety. First we prove an existence theorem for jet differential equations that generalizes a theorem of Diverio. Then we show how one can deduce hyperbolicity for generic complete intersections of high multidegree and high codimension from the known results on hypersurfaces. Finally, motivated by a conjecture of Debarre, we focus on the positivity of the cotangent bundle of complete intersections, and prove some results towards this conjecture; among other things, we prove that a generic complete intersection surface of high multidegree in a projective space of dimension at least four has an ample cotangent bundle.

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27

Wasike, Adu A. M. "Stability and Persistence of Synchronization in a System with a Diffusive-Time-Lag Coupling." Sultan Qaboos University Journal for Science [SQUJS] 13 (June 1, 2008): 33. http://dx.doi.org/10.24200/squjs.vol13iss0pp33-41.

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We study synchronization in the framework of invariant manifold theory for systems with a time lag. Normal hyperbolicity and its persistence in infinite dimensional dynamical systems in Banach spaces is applied to give general results on synchronization and its stability.

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28

Palis, J. "New Developments in Dynamics: Hyperbolicity and Chaotic Dynamics." Symposium - International Astronomical Union 152 (1992): 363–68. http://dx.doi.org/10.1017/s0074180900091397.

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Two important theories in Dynamical Systems were constructed in the sixties: the hyperbolic theory for general systems and the KAM (after Kolmogorov, Arnold and Moser) theory for conservative systems as the ones that appear in Celestial Mechanics. Most of our discussions here concern dissipative (or locally dissipative) systems, although most questions are now being posed for area preserving maps (symplectic maps in higher dimensions). Moreover, one can argue that understanding dynamically small dissipative perturbations of conservative systems is of much importance: indeed it has been recently shown that a KAM curve (tori in higher dimension) can be destroyed and in fact engulfed in the basin of attraction of a Hénon-like strange attractor as defined below.

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29

REULA, OSCAR A. "STRONGLY HYPERBOLIC SYSTEMS IN GENERAL RELATIVITY." Journal of Hyperbolic Differential Equations 01, no. 02 (June 2004): 251–69. http://dx.doi.org/10.1142/s0219891604000111.

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We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We then prove that if a system is strongly hyperbolic with respect to a given hypersurface, then it is also strongly hyperbolic with respect to any nearby surface. We then study for how much these hypersurfaces can be deformed and discuss then causality, namely what the maximal propagation speed in any given direction is. In contrast with the symmetric hyperbolic case, for which the proof of causality is geometrical and direct, relaying in energy estimates, the proof for general strongly hyperbolic systems is indirect for it is based in Holmgren's theorem. To show that the concept is needed in the area of general relativity we discuss two results for which the theory of symmetric hyperbolic systems shows to be insufficient. The first deals with the hyperbolicity analysis of systems which are second order in space derivatives; they include certain versions of the ADM and the BSSN families of equations. This analysis is considerably simplified by introducing pseudo-differential first-order evolution equations. Well-posedness for some members of the latter family systems is established by showing they satisfy the strong hyperbolicity property. Furthermore it is shown that many other systems of such families are only weakly hyperbolic, implying they should not be used for numerical modeling. The second result deals with systems having constraints. The question posed is which hyperbolicity properties, if any, are inherited from the original evolution system by the subsidiary system satisfied by the constraint quantities. The answer is that, subject to some condition on the constraints, if the evolution system is strongly hyperbolic then the subsidiary system is also strongly hyperbolic and the causality properties of both are identical.

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30

Barreira, Luis, Carllos Holanda, and Claudia Valls. "Hyperbolicity of delay equations via cocycles." Journal of Difference Equations and Applications 27, no. 6 (June 3, 2021): 922–45. http://dx.doi.org/10.1080/10236198.2021.1950147.

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31

Hernández, Verónica, Domingo Pestana, and José M. Rodríguez. "Bounds on Gromov hyperbolicity constant." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 110, no. 2 (July 14, 2015): 321–42. http://dx.doi.org/10.1007/s13398-015-0235-5.

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32

Ghiglioni, Eduardo, and Yongdo Lim. "Hyperbolicity of the Karcher mean." Linear Algebra and its Applications 643 (June 2022): 196–217. http://dx.doi.org/10.1016/j.laa.2022.02.018.

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33

Stoimenow, A. "Hyperbolicity of the canonical genus two knots." Journal of Symbolic Computation 101 (November 2020): 242–69. http://dx.doi.org/10.1016/j.jsc.2019.08.003.

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34

Haase, Christian, and Nathan Ilten. "Algebraic hyperbolicity for surfaces in toric threefolds." Journal of Algebraic Geometry 30, no. 3 (January 14, 2021): 573–602. http://dx.doi.org/10.1090/jag/770.

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Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic hyperbolicity of very general surfaces in toric threefolds.

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35

Pijaudier-Cabot, G., and Z. P. Bazˇant. "Comment on Hyperbolicity of Wave Problem for Valanis’ Global Damage Theory." Journal of Applied Mechanics 63, no. 3 (September 1, 1996): 843–45. http://dx.doi.org/10.1115/1.2823371.

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36

Rodriguez Hertz, Federico, María Alejandra Rodriguez Hertz, and Raúl Ures. "Partial hyperbolicity and ergodicity in dimension three." Journal of Modern Dynamics 2, no. 2 (2008): 187–208. http://dx.doi.org/10.3934/jmd.2008.2.187.

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37

Rodriguez Hertz, Jana. "Genericity of nonuniform hyperbolicity in dimension 3." Journal of Modern Dynamics 6, no. 1 (2012): 121–38. http://dx.doi.org/10.3934/jmd.2012.6.121.

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38

Shi, Yi, Shaobo Gan, and Lan Wen. "On the singular-hyperbolicity of star flows." Journal of Modern Dynamics 8, no. 2 (2014): 191–219. http://dx.doi.org/10.3934/jmd.2014.8.191.

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39

Hammerlindl, Andy, Jana Rodriguez Hertz, and Raúl Ures. "Ergodicity and partial hyperbolicity on Seifert manifolds." Journal of Modern Dynamics 16 (2020): 331–48. http://dx.doi.org/10.3934/jmd.2020012.

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40

B�tkai, Andr�s. "Hyperbolicity of linear partial differential equations with delay." Integral Equations and Operator Theory 44, no. 4 (December 2002): 383–96. http://dx.doi.org/10.1007/bf01193667.

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41

Wu, Jingcao. "The Injectivity Theorem on a Non-Compact Kähler Manifold." Symmetry 13, no. 11 (November 20, 2021): 2222. http://dx.doi.org/10.3390/sym13112222.

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In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in Cn, hyperconvex bounded domains, and so on.

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42

Federici, Bruno, and Agelos Georgakopoulos. "Hyperbolicity vs. Amenability for Planar Graphs." Discrete & Computational Geometry 58, no. 1 (February 14, 2017): 67–79. http://dx.doi.org/10.1007/s00454-017-9859-x.

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43

Kuo, Jung-Miao, and Su Chi Wen. "Hyperbolicity of algebras with involution over a given extension." Journal of Pure and Applied Algebra 215, no. 6 (June 2011): 1348–59. http://dx.doi.org/10.1016/j.jpaa.2010.08.015.

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44

Potrie, Rafael. "Partial hyperbolicity and foliations in $\mathbb{T}^3$." Journal of Modern Dynamics 9, no. 01 (2015): 81–121. http://dx.doi.org/10.3934/jmd.2015.9.81.

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45

Wasike, Adu A. M., and K. T. Rotich. "Synchronization and persistence in Diffusively Coupled Lattice Oscillators." Sultan Qaboos University Journal for Science [SQUJS] 12, no. 1 (June 1, 2007): 41. http://dx.doi.org/10.24200/squjs.vol12iss1pp41-52.

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We consider the synchronization and persistence of a system of identical lattice oscillators that are diffusively coupled to their nearest neighbours. Each subsystem has a compact global attractor. This is done in the framework of invariant manifold theory. Normal hyperbolicity and its persistence are applied to obtain general conditions for the stability and robustness of the synchronization manifold. AMS(MOS) Subject classifications: 37C80, 37D10.

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46

Quéguiner-Mathieu, Anne, and Jean-Pierre Tignol. "Cohomological invariants for orthogonal involutions on degree 8 algebras." Journal of K-Theory 9, no. 2 (July 5, 2011): 333–58. http://dx.doi.org/10.1017/is011006015jkt160.

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AbstractUsing triality, we define a relative Arason invariant for orthogonal involutions on a -possibly division- central simple algebra of degree 8. This invariant detects hyperbolicity, but it does not detect isomorphism. We produce explicit examples, in index 4 and 8, of non isomorphic involutions with trivial relative Arason invariant.

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47

Amini, Nima. "Spectrahedrality of hyperbolicity cones of multivariate matching polynomials." Journal of Algebraic Combinatorics 50, no. 2 (October 16, 2018): 165–90. http://dx.doi.org/10.1007/s10801-018-0848-9.

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48

CALIXTO, M., V. ALDAYA, and M. NAVARRO. "QUANTUM FIELD THEORY IN A SYMMETRIC CURVED SPACE FROM A SECOND QUANTIZATION ON A GROUP." International Journal of Modern Physics A 15, no. 25 (October 10, 2000): 4011–44. http://dx.doi.org/10.1142/s0217751x00001233.

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In this paper we propose a "second quantization" scheme especially suitable for dealing with nontrivial, highly symmetric phase spaces, implemented within a more general group approach to quantization, which recovers the standard quantum field theory (QFT) for ordinary relativistic linear fields. We emphasize, among its main virtues, greater suitability in characterizing vacuum states in a QFT on a highly symmetric curved space–time and the absence of the usual requirement of global hyperbolicity. This can be achieved in the special case of the Anti-de Sitter universe, on which we explicitly construct a QFT.

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49

Popa, Mihnea, Behrouz Taji, and Lei Wu. "Brody hyperbolicity of base spaces of certain families of varieties." Algebra & Number Theory 13, no. 9 (December 7, 2019): 2205–42. http://dx.doi.org/10.2140/ant.2019.13.2205.

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50

Gray, Robert D., and Mark Kambites. "A strong geometric hyperbolicity property for directed graphs and monoids." Journal of Algebra 420 (December 2014): 373–401. http://dx.doi.org/10.1016/j.jalgebra.2014.08.007.

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