Topological Signals of Singularities in Ricci Flow
暂无分享,去创建一个
Konstantin Mischaikow | Gordon Jones | Howard A. Blair | Paul M. Alsing | Warner A. Miller | Vidit Nanda | Matthew Corne | K. Mischaikow | Vidit Nanda | H. A. Blair | P. Alsing | W. Miller | Matthew Corne | Gordon Jones
[1] Steve Oudot,et al. The Structure and Stability of Persistence Modules , 2012, Springer Briefs in Mathematics.
[2] P. Alsing,et al. Equivalence of Simplicial Ricci Flow and Hamilton's Ricci Flow for 3D Neckpinch Geometries , 2014, 1404.4055.
[3] F. Verstraete,et al. Geometry of Matrix Product States: metric, parallel transport and curvature , 2012, 1210.7710.
[4] Robin Forman,et al. Bochner's Method for Cell Complexes and Combinatorial Ricci Curvature , 2003, Discret. Comput. Geom..
[5] Warner A. Miller. The geometrodynamic content of the Regge equations as illuminated by the boundary of a boundary principle , 1986 .
[6] S. Sherwin,et al. Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations , 2005 .
[7] Radmila Sazdanovic,et al. Simplicial Models and Topological Inference in Biological Systems , 2014, Discrete and Topological Models in Molecular Biology.
[8] W. Miller,et al. A geometric construction of the Riemann scalar curvature in Regge calculus , 2008, 0805.2411.
[9] W. Thurston,et al. Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.
[10] Shing-Tung Yau,et al. Fundamentals of Computational Conformal Geometry , 2010, Math. Comput. Sci..
[11] Maximilian Kreuzer,et al. Geometry, Topology and Physics I , 2009 .
[12] Vijay Kumar,et al. Persistent Homology for Path Planning in Uncertain Environments , 2015, IEEE Transactions on Robotics.
[13] Peter John Wood,et al. Ieee Transactions on Pattern Analysis and Machine Intelligence Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images , 2022 .
[14] D. Glickenstein,et al. Discrete conformal variations and scalar curvature on piecewise flat two and three dimensional manifolds , 2009, 0906.1560.
[15] Konstantin Mischaikow,et al. Evolution of force networks in dense particulate media. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.
[16] R. Forman. Morse Theory for Cell Complexes , 1998 .
[17] S. Yau,et al. Simplicial Ricci Flow , 2013, 1302.0804.
[18] Ginestra Bianconi,et al. Entropy measures for networks: toward an information theory of complex topologies. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.
[19] Jie Gao,et al. Scalable routing in 3D high genus sensor networks using graph embedding , 2012, 2012 Proceedings IEEE INFOCOM.
[20] W. Wootters,et al. Distributed Entanglement , 1999, quant-ph/9907047.
[21] D. A. Stone,et al. Sectional curvature in piecewise linear manifolds , 1973 .
[22] R. Hamilton. Three-manifolds with positive Ricci curvature , 1982 .
[23] P. Baird. The Ricci flow: techniques and applications -Part I: Geometric aspects (Mathematical Surveys and Monographs 135) , 2008 .
[24] Konstantin Mischaikow,et al. Morse Theory for Filtrations and Efficient Computation of Persistent Homology , 2013, Discret. Comput. Geom..
[25] Sigurd B. Angenent,et al. Degenerate neckpinches in Ricci flow , 2012 .
[26] R. Hamilton,et al. The formations of singularities in the Ricci Flow , 1993 .
[27] E. Woolgar,et al. Some Applications of Ricci Flow in Physics , 2007, 0708.2144.
[28] Adam Watkins,et al. Topological and statistical behavior classifiers for tracking applications , 2014, IEEE Transactions on Aerospace and Electronic Systems.
[29] Vin de Silva,et al. Coverage in sensor networks via persistent homology , 2007 .
[30] Mark Van Raamsdonk. Building up spacetime with quantum entanglement , 2010 .
[31] Robert Schrader,et al. On the curvature of piecewise flat spaces , 1984 .
[32] Emil Saucan,et al. Metric Ricci curvature for $PL$ manifolds , 2012, ArXiv.
[33] H. Edelsbrunner,et al. Persistent Homology — a Survey , 2022 .
[34] Mauro Carfora,et al. The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow , 2014 .
[35] R. Ghrist. Barcodes: The persistent topology of data , 2007 .
[36] W. Thurston,et al. Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.
[37] Huabin Ge,et al. Discrete quasi-Einstein metrics and combinatorial curvature flows in 3-dimension , 2013, 1301.3398.
[38] B. Chow,et al. COMBINATORIAL RICCI FLOWS ON SURFACES , 2002, math/0211256.
[39] Dan Knopf,et al. An example of neckpinching for Ricci flow on $S^{n+1}$ , 2004 .
[40] R. Ho. Algebraic Topology , 2022 .
[41] Sigurd B. Angenent,et al. Formal matched asymptotics for degenerate Ricci flow neckpinches , 2011 .
[42] Mauro Carfora,et al. Renormalization Group and the Ricci Flow , 2010, 1001.3595.
[43] G. Perelman. Ricci flow with surgery on three-manifolds , 2003, math/0303109.
[44] Peng Lu,et al. The Ricci Flow: Techniques and Applications , 2007 .
[45] Aaron Trout. Positively Curved Combinatorial 3-Manifolds , 2010, Electron. J. Comb..
[46] Scott N. Walck,et al. Topology of the three-qubit space of entanglement types , 2005 .
[47] P. Alsing,et al. The Simplicial Ricci Tensor , 2011, 1107.2458.
[48] Afra Zomorodian,et al. Computing Persistent Homology , 2004, SCG '04.
[49] Anil N. Hirani,et al. Discrete exterior calculus , 2005, math/0508341.
[50] M. Raamsdonk,et al. Building up spacetime with quantum entanglement , 2010, 1005.3035.
[51] Herbert Edelsbrunner,et al. Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web , 2013, Trans. Comput. Sci..
[52] R. Bishop,et al. Tensor Analysis on Manifolds , 1980 .
[53] Richard Friedberg,et al. Derivation of Regge's action from Einstein's theory of general relativity☆ , 1984 .
[54] Alexander Russell,et al. Computational topology: ambient isotopic approximation of 2-manifolds , 2003, Theor. Comput. Sci..
[55] G. Perelman. The entropy formula for the Ricci flow and its geometric applications , 2002, math/0211159.
[56] B. Chow,et al. The Ricci Flow : An Introduction I , 2013 .
[57] J. Jost,et al. Network Topology vs. Geometry: From persistent Homology to Curvature , 2017 .
[58] D. Glickenstein. Geometric triangulations and discrete Laplacians on manifolds , 2005, math/0508188.
[59] Mauro Carfora,et al. Ricci Flow Conjugated Initial Data Sets for Einstein Equations , 2010, 1006.1500.
[60] S. Yau,et al. On exterior calculus and curvature in piecewise-flat manifolds , 2012, 1212.0919.
[61] Warner A. Miller,et al. A Fully (3+1)-D Regge calculus model of the Kasner cosmology , 1997, gr-qc/9706034.
[62] Warner A. Miller. The Hilbert action in Regge calculus , 1997 .
[63] David Garfinkle,et al. The Modelling of Degenerate Neck Pinch Singularities in Ricci Flow by Bryant Solitons , 2007 .
[64] Huiling Gu,et al. The Existence of Type II Singularities for the Ricci Flow on $S^{n+1}$ , 2007, 0707.0033.
[65] M. Carfora. The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow , 2014, 1405.0827.
[66] T. Regge. General relativity without coordinates , 1961 .
[67] Gunnar E. Carlsson,et al. Topology and data , 2009 .