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Books on the topic 'Elliptic manifold'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Kirk, P. Analytic deformations of the spectrum of a family of Dirac operators on an odd-dimensional manifold with boundary. Providence, RI: American Mathematical Society, 1996.

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2

Elliptic structures on 3-manifolds. Cambridge [Cambridgeshire]: Cambridge University Press, 1986.

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3

Hong, Sungbok. Diffeomorphisms of Elliptic 3-Manifolds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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4

Hong, Sungbok, John Kalliongis, Darryl McCullough, and J. Hyam Rubinstein. Diffeomorphisms of Elliptic 3-Manifolds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31564-0.

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5

Nazaĭkinskiĭ, V. E. Elliptic theory on singular manifolds. Boca Raton: Chapman & Hall/CRC, 2006.

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6

1953-, Pinchover Yehuda, ed. Manifolds with group actions and elliptic operators. Providence, R.I: American Mathematical Society, 1994.

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7

Schapira, Pierre. Index theorem for elliptic pairs. Paris: Société mathématique de France, 1994.

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8

1922-, Markus L., ed. Elliptic partial differential operators and symplectic algebra. Providence, RI: American Mathematical Society, 2003.

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9

Compactness and stability for nonlinear elliptic equations. Zürich, Switzerland: European Mathematical Society, 2014.

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10

Werner, Müller. L²-index of elliptic operators on manifolds with cusps of rank one. Berlin: Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik, 1985.

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11

Elliptic genera and vertex operator super-algebras. Berlin: Springer, 1999.

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12

Mielke, Alexander. Hamiltonian and Lagrangian flows on center manifolds: With applications to elliptic variational problems. Berlin: Springer-Verlag, 1991.

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13

Nicolaescu, Liviu I. Generalized symplectic geometries and the index of families of elliptic problems. Providence, R.I: American Mathematical Society, 1997.

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14

Schulze, Bert-Wolfgang. Differential equations on singular manifolds: Semiclassical theory and operator algebras. Berlin: Wiley-VCH, 1998.

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15

Bert-Wolfgang, Schulze, ed. Crack theory and edge singularities. Boston: Kluwer Academic Publishers, 2003.

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16

Schulze, Bert-Wolfgang. Corner Mellin operators and reduction of orders with parameters. Berlin: Akademie der Wissenschaften der DDR, Karl-Weierstras-Institut für Mathematik, 1988.

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17

1963-, Pantev Tony, ed. Torus fibrations, gerbes, and duality. Providence, R.I: American Mathematical Society, 2008.

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18

author, Tkachev Vladimir 1963, and Vlăduț, S. G. (Serge G.), 1954- author, eds. Nonlinear elliptic equations and nonassociative algebras. Providence, Rhode Island: American Mathematical Society, 2014.

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19

1943-, Gossez J. P., and Bonheure Denis, eds. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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20

P, Minicozzi William, ed. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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21

1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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22

Jakobson, Dmitry, Pierre Albin, and Frédéric Rochon. Geometric and spectral analysis. Providence, Rhode Island: American Mathematical Society, 2014.

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23

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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24

Topological modular forms. Providence, Rhode Island: American Mathematical Society, 2014.

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25

Nahmod, Andrea R. Recent advances in harmonic analysis and partial differential equations: AMS special sessions, March 12-13, 2011, Statesboro, Georgia : the JAMI Conference, March 21-25, 2011, Baltimore, Maryland. Edited by American Mathematical Society and JAMI Conference (2011 : Baltimore, Md.). Providence, Rhode Island: American Mathematical Society, 2012.

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26

Angelo, Iollo, and Langley Research Center, eds. On the circulation manifold for two adjacent lifting sections. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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27

Epstein, Charles L., and Rafe Mazzeo. Maximum Principles and Uniqueness Theorems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0003.

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This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both for the model operators on an open orthant and for the general Kimura diffusion operators on a compact manifold with corners, as well as their elliptic analogues. Of particular note in this regard is a generalization of the Hopf boundary point maximum principle. The chapter first presents maximum principles for the model operators before discussing Kimura diffusion operators on manifolds with corners. It then describes maximum principles for the heat equation as well as the corresponding maximum principle and uniqueness result for Kimura diffusion equations.

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28

Epstein, Charles L., and Rafe Mazzeo. Wright-Fisher Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0002.

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This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural domains of definition for generalized Kimura diffusions: polyhedra in Euclidean space or, more generally, abstract manifolds with corners. Amongst the convex polyhedra, the chapter distinguishes the subclass of regular convex polyhedra P. P is a regular convex polyhedron if it is convex and if near any corner, P is the intersection of no more than N half-spaces with corresponding normal vectors that are linearly independent. These definitions establish that any regular convex polyhedron is a manifold with corners. The chapter concludes by defining the general class of elliptic Kimura operators on a manifold with corners P and shows that there is a local normal form for any operator L in this class.

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29

Carlson, James. Period Domains and Period Mappings. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0004.

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This chapter seeks to develop a working understanding of the notions of period domain and period mapping, as well as familiarity with basic examples thereof. It first reviews the notion of a polarized Hodge structure H of weight n over the integers, for which the motivating example is the primitive cohomology in dimension n of a projective algebraic manifold of the same dimension. Next, the chapter presents lectures on period domains and monodromy, as well as elliptic curves. Hereafter, the chapter provides an example of period mappings, before considering Hodge structures of weight. After expounding on Poincaré residues, this chapter establishes some properties of the period mapping for hypersurfaces and the Jacobian ideal and the local Torelli theorem. Finally, the chapter studies the distance-decreasing properties and integral manifolds of the horizontal distribution.

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30

Nazaikinskii, Vladimir E., Bert-Wolfgang Schulze, Boris Yu Sternin, and Anton Yu Savin. Elliptic Theory on Singular Manifolds. Taylor & Francis Group, 2005.

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31

Nazaikinskii, Vladimir E., Bert-Wolfgang Schulze, Boris Yu Sternin, and Anton Yu Savin. Elliptic Theory on Singular Manifolds. Taylor & Francis Group, 2019.

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32

Thomas, Charles Benedict. Elliptic Structures On 3-Manifolds. Cambridge University Press, 2011.

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33

Thomas, Charles Benedict. Elliptic Structures On 3-Manifolds. Cambridge University Press, 2010.

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34

Schulze, Bert-Wolfgang, Boris Sternin, and Vladimir Nazaikinskii. Localization Problem in Index Theory of Elliptic Operators. Birkhauser Verlag, 2013.

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35

The Localization Problem In Index Theory Of Elliptic Operators. Springer Basel, 2013.

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36

Elliptic Theory on Singular Manifolds (Differential and Integral Equations and Their Applications). Chapman & Hall/CRC, 2005.

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37

Fredholm Operators And Einstein Metrics on Conformally Compact Manifolds (Memoirs of the American Mathematical Society). American Mathematical Society, 2006.

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38

Nazaikinskii, Vladimir E. Elliptic Theory on Singular Manifolds. Differential and Integral Equations and Their Applications. Taylor & Francis Group, 2006.

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39

Epstein, Charles L., and Rafe Mazzeo. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0001.

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This book proves the existence, uniqueness and regularity results for a class of degenerate elliptic operators known as generalized Kimura diffusions, which act on functions defined on manifolds with corners. It presents a generalization of the Hopf boundary point maximum principle that demonstrates, in the general case, how regularity implies uniqueness. The book is divided in three parts. Part I deals with Wright–Fisher geometry and the maximum principle; Part II is devoted to an analysis of model problems, and includes degenerate Hölder spaces; and Part III discusses generalized Kimura diffusions. This introductory chapter provides an overview of generalized Kimura diffusions and their applications in probability theory, model problems, perturbation theory, main results, and alternate approaches to the study of similar degenerate elliptic and parabolic equations.

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40

Mielke, Alexander. Hamiltonian and Lagrangian Flows on Center Manifolds: With Applications to Elliptic Variational Problems. Springer London, Limited, 2006.

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41

Ivrii, Victor. Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds with Boundary. Springer London, Limited, 2006.

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42

Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.

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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.

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43

Mitrea, Dorina, Marius Mitrea, and Michael Taylor. Layer Potentials, the Hodge Laplacian, and Global Boundary Problems in Nonsmooth Reimannian Manifolds (Memoirs of the American Mathematical Society). American Mathematical Society, 2001.

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44

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

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45

Nier, Francis. Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries. American Mathematical Society, 2018.

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46

Robbiano, Luc, Gilles Lebeau, and Jérôme Le Rousseau. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II: General Boundary Conditions on Riemannian Manifolds. Springer International Publishing AG, 2022.

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47

Pascal, Auscher, Coulhon T, and Grigoryan A, eds. Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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48

Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs : April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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49

George C. Marshall Space Flight Center, ed. Viscous flow computations for elliptical two-duct version of the SSME hot gas manifold: Interim report. [Huntsville?], AL: National Aeronautics and Space Administration, Marshall Space Flight Center, 1986.

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50

Non-Linear Elliptic Equations in Conformal Geometry (Zurich Lectures in Advanced Mathematics). European Mathematical Society, 2004.

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