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Journal articles on the topic 'Splitting theorem'

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Published: 9 March 2023
Last updated: 10 March 2023

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1

Anderson, Michael T. "splitting theorem." Duke Mathematical Journal 68, no. 1 (October 1992): 67–82. http://dx.doi.org/10.1215/s0012-7094-92-06803-7.

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2

Camillo, Victor. "On Zimmermann-Huisgen's Splitting Theorem." Proceedings of the American Mathematical Society 94, no. 2 (June 1985): 206. http://dx.doi.org/10.2307/2045375.

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3

Wu, Guoqiang. "Splitting theorem for Ricci soliton." Proceedings of the American Mathematical Society 149, no. 8 (May 18, 2021): 3575–81. http://dx.doi.org/10.1090/proc/15466.

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Let ( M , g , f ) (M, g, f) be a gradient Ricci soliton ∇ 2 f + R i c = λ g \nabla ^2 f+Ric=\lambda g with λ ∈ { 1 2 , 0 , − 1 2 } \lambda \in \{\frac {1}{2}, 0, -\frac {1}{2}\} . Suppose there is a geodesic line γ : ( − ∞ , ∞ ) → M \gamma : (-\infty , \infty )\rightarrow M satisfying lim inf t → ∞ ∫ 0 t R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s + lim inf t → − ∞ ∫ t 0 R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s ≥ 0 , \begin{eqnarray*} \liminf _{t\rightarrow \infty }\int _0^{t}Ric(\gamma ’(s), \gamma ’(s))ds +\liminf _{t\rightarrow -\infty }\int _{t}^{0}Ric(\gamma ’(s), \gamma ’(s))ds \geq 0, \end{eqnarray*} then ( M , g , f ) (M, g, f) splits off a line isometrically.
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4

Croke, Christopher B., and Bruce Kleiner. "A warped product splitting theorem." Duke Mathematical Journal 67, no. 3 (September 1992): 571–74. http://dx.doi.org/10.1215/s0012-7094-92-06723-8.

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5

Lempp, Steffen, and Sui Yuefei. "An extended Lachlan splitting theorem." Annals of Pure and Applied Logic 79, no. 1 (May 1996): 53–59. http://dx.doi.org/10.1016/0168-0072(95)00039-9.

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6

Covolo, Tiffany, Janusz Grabowski, and Norbert Poncin. "Splitting theorem for Z2n-supermanifolds." Journal of Geometry and Physics 110 (December 2016): 393–401. http://dx.doi.org/10.1016/j.geomphys.2016.09.006.

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7

Borzellino, Joseph E., and Shun-Hui Zhu. "The splitting theorem for orbifolds." Illinois Journal of Mathematics 38, no. 4 (December 1994): 679–91. http://dx.doi.org/10.1215/ijm/1256060999.

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8

Camillo, Victor. "On Zimmermann-Huisgen’s splitting theorem." Proceedings of the American Mathematical Society 94, no. 2 (February 1, 1985): 206. http://dx.doi.org/10.1090/s0002-9939-1985-0784163-6.

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9

Szigeti, Zoltán. "On the local splitting theorem." Electronic Notes in Discrete Mathematics 19 (June 2005): 57–61. http://dx.doi.org/10.1016/j.endm.2005.05.009.

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10

Li, Chong, Shujie Li, and Jiaquan Liu. "Splitting theorem, Poincaré–Hopf theorem and jumping nonlinear problems." Journal of Functional Analysis 221, no. 2 (April 2005): 439–55. http://dx.doi.org/10.1016/j.jfa.2004.09.010.

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11

GONZÁLEZ-TOKMAN, CECILIA, and ANTHONY QUAS. "A semi-invertible operator Oseledets theorem." Ergodic Theory and Dynamical Systems 34, no. 4 (March 11, 2013): 1230–72. http://dx.doi.org/10.1017/etds.2012.189.

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AbstractSemi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition of piecewise expanding interval maps randomly chosen from a set of cardinality of the continuum. We also give an application of the theorem to random compositions of perturbations of an expanding map in higher dimensions.
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12

Loustaunau, Philippe. "A splitting theorem for ℱ-products." Fundamenta Mathematicae 136, no. 2 (1990): 73–83. http://dx.doi.org/10.4064/fm-136-2-73-83.

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13

Kontostathis, Kyriakos. "The combinatorics of the splitting theorem." Journal of Symbolic Logic 62, no. 1 (March 1997): 197–224. http://dx.doi.org/10.2307/2275739.

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The complexity of priority proofs in recursion theory has been growing since the first priority proofs in [1] and [11]. Refined versions of classic priority proofs can be found in [18]. To this date, this part of recursion theory is at about the same stage of development as real analysis was in the early days, when the notions of topology, continuity, compactness, vector space, inner product space, etc., were not invented. There were no general theorems involving these concepts to prove results about the real numbers and the proofs were repetitive and lengthy.The priority method contains an unprecedent wealth of combinatorics which is used to answer questions in recursion theory and is bound to have applications in many other fields as well. Unfortunately, very little progress has been made in finding theorems to formulate the combinatorial part of the priority method so as to answer questions without having to reprove the combinatorics in each case.Lempp and Lerman in [10] provide an overview of the subject. The entire edifice of definitions and theorems which formulate the combinatorics of the priority method has acquired the name Priority Theory. From a different vein, Groszek and Slaman in [2] have initiated a program to classify priority constructions in terms of how much induction or collection is needed to carry them out. This program studies the complexity of priority proofs and can be called Complexity Theory of Priority Proofs or simply Complexity.
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14

Winkler, R. "Rashba spin splitting and Ehrenfest's theorem." Physica E: Low-dimensional Systems and Nanostructures 22, no. 1-3 (April 2004): 450–54. http://dx.doi.org/10.1016/j.physe.2003.12.043.

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15

Biswas, Indranil, Mahan Mj, and A. Parameswaran. "A splitting theorem for good complexifications." Annales de l’institut Fourier 66, no. 5 (2016): 1965–85. http://dx.doi.org/10.5802/aif.3054.

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16

Mashiko, Yukihiro. "A splitting theorem for Alexandrov spaces." Pacific Journal of Mathematics 204, no. 2 (June 1, 2002): 445–58. http://dx.doi.org/10.2140/pjm.2002.204.445.

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17

Huang, Hongnian. "A splitting theorem on toric manifolds." Mathematical Research Letters 20, no. 2 (2013): 273–78. http://dx.doi.org/10.4310/mrl.2013.v20.n2.a5.

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18

Alsedà, Ll, M. A. del Rı́o, and J. A. Rodrı́guez. "A Splitting Theorem for Transitive Maps." Journal of Mathematical Analysis and Applications 232, no. 2 (April 1999): 359–75. http://dx.doi.org/10.1006/jmaa.1999.6277.

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19

Chodosh, Otis, Michael Eichmair, and Vlad Moraru. "A Splitting Theorem for Scalar Curvature." Communications on Pure and Applied Mathematics 72, no. 6 (December 14, 2018): 1231–42. http://dx.doi.org/10.1002/cpa.21803.

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20

Nguyen, Thang, and Shi Wang. "Cheeger–Gromoll splitting theorem for groups." Algebraic & Geometric Topology 22, no. 7 (December 31, 2022): 3377–99. http://dx.doi.org/10.2140/agt.2022.22.3377.

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21

PETRONIO, CARLO. "Spherical splitting of 3-orbifolds." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 2 (March 2007): 269–87. http://dx.doi.org/10.1017/s0305004106009807.

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AbstractThe famous Haken–Kneser–Milnor theorem states that every 3-manifold can be expressed in a unique way as a connected sum of prime 3-manifolds. The analogous statement for 3-orbifolds has been part of the folklore for several years, and it was commonly believed that slight variations on the argument used for manifolds would be sufficient to establish it. We demonstrate in this paper that this is not the case, proving that the apparently natural notion of “essential” system of spherical 2-orbifolds is not adequate in this context. We also show that the statement itself of the theorem must be given in a substantially different way. We then prove the theorem in full detail, using a certain notion of “efficient splitting system.”
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22

Dung, Nguyen Thac, and Chiung-Jue Anna Sung. "Analysis of weighted p-harmonic forms and applications." International Journal of Mathematics 30, no. 11 (October 2019): 1950058. http://dx.doi.org/10.1142/s0129167x19500587.

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In this paper, we study weighted [Formula: see text]-harmonic forms on smooth metric measure space [Formula: see text] with a weighted Sobolev or a weighted Poincaré inequality. When [Formula: see text] is constant, we derive a splitting theorem for Kähler manifolds with maximal bottom spectrum for the [Formula: see text]-Laplacian. For general [Formula: see text] we also obtain various splitting and vanishing theorems when the weighted curvature operator of [Formula: see text] is bounded below. As applications, we conclude Liouville property for weighted [Formula: see text]-harmonic functions and [Formula: see text]-harmonic maps.
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23

Betley, Stanislaw. "Splitting Theorem for Homology of GL(R)." Proceedings of the American Mathematical Society 108, no. 2 (February 1990): 297. http://dx.doi.org/10.2307/2048275.

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24

Simson, Daniel. "A splitting theorem for multipeak path algebras." Fundamenta Mathematicae 138, no. 2 (1991): 113–37. http://dx.doi.org/10.4064/fm-138-2-113-137.

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25

Yun, Jong-Gug. "A GENERALIZATION OF THE LORENTZIAN SPLITTING THEOREM." Bulletin of the Korean Mathematical Society 49, no. 3 (May 31, 2012): 647–53. http://dx.doi.org/10.4134/bkms.2012.49.3.647.

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26

Shi, Hongbo. "A Graph Approach to a Splitting Theorem." Algebra Colloquium 13, no. 01 (March 2006): 57–66. http://dx.doi.org/10.1142/s1005386706000095.

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By associating a graph to the ring under discussion, we propose a graph approach to extend a well-known ring splitting theorem due to Zaks, and we then describe the global and finitistic dimensions of the ring in the language of the graph.
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27

Shore, Richard A., and Theodore A. Slaman. "A splitting theorem for $n-REA$ degrees." Proceedings of the American Mathematical Society 129, no. 12 (April 25, 2001): 3721–28. http://dx.doi.org/10.1090/s0002-9939-01-06015-4.

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28

Bleybel, Ali. "A Temporal Splitting Theorem for Chronological Spaces." Gravitation and Cosmology 28, no. 4 (November 25, 2022): 362–74. http://dx.doi.org/10.1134/s0202289322040041.

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29

González, S., C. Martínez, and A. Grishkov. "A radical splitting theorem for bernstein algebras." Communications in Algebra 26, no. 8 (January 1998): 2529–42. http://dx.doi.org/10.1080/00927879808826296.

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30

Yi, Xiaoding. "A non-splitting theorem for d.r.e. sets." Annals of Pure and Applied Logic 82, no. 1 (November 1996): 17–96. http://dx.doi.org/10.1016/0168-0072(95)00070-4.

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31

Kultze, Rolf. "A splitting theorem for connected moravaK-theories." Manuscripta Mathematica 69, no. 1 (December 1990): 31–42. http://dx.doi.org/10.1007/bf02567911.

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32

Alexander, Stephanie, and Richard Bishop. "A cone splitting theorem for Alexandrov spaces." Pacific Journal of Mathematics 218, no. 1 (January 1, 2005): 1–15. http://dx.doi.org/10.2140/pjm.2005.218.1.

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33

Apostolov, Vestislav, and Hongnian Huang. "A Splitting Theorem for Extremal Kähler Metrics." Journal of Geometric Analysis 25, no. 1 (April 12, 2013): 149–70. http://dx.doi.org/10.1007/s12220-013-9417-6.

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34

Kim, Jaehong. "A splitting theorem for holomorphic Banach bundles." Mathematische Zeitschrift 263, no. 1 (September 2, 2008): 89–102. http://dx.doi.org/10.1007/s00209-008-0411-9.

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35

Wang, Lin Feng. "A splitting theorem for the weighted measure." Annals of Global Analysis and Geometry 42, no. 1 (November 13, 2011): 79–89. http://dx.doi.org/10.1007/s10455-011-9302-0.

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36

Kourousias, George, and David Makinson. "Parallel interpolation, splitting, and relevance in belief change." Journal of Symbolic Logic 72, no. 3 (September 2007): 994–1002. http://dx.doi.org/10.2178/jsl/1191333851.

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AbstractThe splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGM partial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh's relevance criterion.
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37

MORIAH, YOAV, and ERIC SEDGWICK. "CLOSED ESSENTIAL SURFACES AND WEAKLY REDUCIBLE HEEGAARD SPLITTINGS IN MANIFOLDS WITH BOUNDARY." Journal of Knot Theory and Its Ramifications 13, no. 06 (September 2004): 829–43. http://dx.doi.org/10.1142/s0218216504003470.

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We show that there are infinitely many two component links in S3 whose complements have weakly reducible and irreducible non-minimal genus Heegaard splittings, yet the construction given in the theorem of Casson and Gordon does not produce an essential closed surface. The situation for manifolds with a single boundary component is still unresolved though we obtain partial results regarding manifolds with a non-minimal genus weakly reducible and irreducible Heegaard splitting.
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38

De Stefani, Alessandro, Thomas Polstra, and Yongwei Yao. "Generalizing Serre’s Splitting Theorem and Bass’s Cancellation Theorem via free-basic elements." Proceedings of the American Mathematical Society 146, no. 4 (December 26, 2017): 1417–30. http://dx.doi.org/10.1090/proc/13754.

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39

BARNES, DONALD W. "ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS." Bulletin of the Australian Mathematical Society 86, no. 2 (November 30, 2011): 184–85. http://dx.doi.org/10.1017/s0004972711002954.

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AbstractA Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.
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40

Case, Jeffrey S. "Singularity theorems and the Lorentzian splitting theorem for the Bakry–Emery–Ricci tensor." Journal of Geometry and Physics 60, no. 3 (March 2010): 477–90. http://dx.doi.org/10.1016/j.geomphys.2009.11.001.

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41

Moriyama, Takayuki, and Takashi Nitta. "Splitting theorem for sheaves of holomorphic k-vectors on complex contact manifolds." International Journal of Mathematics 29, no. 13 (December 2018): 1850091. http://dx.doi.org/10.1142/s0129167x1850091x.

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A complex contact structure [Formula: see text] is defined by a system of holomorphic local 1-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle [Formula: see text] of the tangent bundle and a line bundle [Formula: see text]. In this paper, we prove that the sheaf of holomorphic [Formula: see text]-vectors on a complex contact manifold splits into the sum of [Formula: see text] and [Formula: see text] as sheaves of [Formula: see text]-module. The theorem induces the short exact sequence of cohomology of holomorphic [Formula: see text]-vectors, and we obtain vanishing theorems for the cohomology of [Formula: see text].
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42

Cooper, S. Barry. "A Splitting Theorem for the N-R.E. Degrees." Proceedings of the American Mathematical Society 115, no. 2 (June 1992): 461. http://dx.doi.org/10.2307/2159269.

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43

Koike, Naoyuki. "A splitting theorem for proper complex equifocal submanifolds." Tohoku Mathematical Journal 58, no. 3 (September 2006): 393–417. http://dx.doi.org/10.2748/tmj/1163775137.

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44

Kuwae, Kazuhiro, and Takashi Shioya. "A topological splitting theorem for weighted Alexandrov spaces." Tohoku Mathematical Journal 63, no. 1 (2011): 59–76. http://dx.doi.org/10.2748/tmj/1303219936.

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45

Ullman, Harry E. "An equivariant generalization of the Miller splitting theorem." Algebraic & Geometric Topology 12, no. 2 (April 8, 2012): 643–84. http://dx.doi.org/10.2140/agt.2012.12.643.

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46

Kath, Ines, and Paul-Andi Nagy. "A splitting theorem for higher order parallel immersions." Proceedings of the American Mathematical Society 140, no. 8 (August 1, 2012): 2873–82. http://dx.doi.org/10.1090/s0002-9939-2011-11342-x.

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47

Betley, Stanisław. "Splitting theorem for homology of ${\rm GL}(R)$." Proceedings of the American Mathematical Society 108, no. 2 (February 1, 1990): 297. http://dx.doi.org/10.1090/s0002-9939-1990-0984782-x.

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48

Cooper, S. Barry. "A splitting theorem for the $n$-r.e.\ degrees." Proceedings of the American Mathematical Society 115, no. 2 (February 1, 1992): 461. http://dx.doi.org/10.1090/s0002-9939-1992-1105037-0.

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49

Schroeder, Viktor. "A splitting theorem for spaces of nonpositive curvature." Inventiones Mathematicae 79, no. 2 (June 1985): 323–27. http://dx.doi.org/10.1007/bf01388977.

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50

Itoh, Kazuki. "A topological splitting theorem for sub-Riemannian manifolds." Geometriae Dedicata 168, no. 1 (January 10, 2013): 177–96. http://dx.doi.org/10.1007/s10711-012-9824-z.

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