Simplicial Ricci flow

DOI10.1007/s00220-014-1911-6zbMath1295.53076arXiv1302.0804OpenAlexW2157104589MaRDI QIDQ2249759

Jonathan R. McDonald, Warner Allen Miller, David Xianfeng Gu, Shing Tung Yau, Paul M. Alsing

Publication date: 3 July 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0804

zbMATH Keywords

Regge calculusHamilton's Ricci flowdiscrete exterior calculusPoincaré conjecturedual-edge Regge-Ricci flowpiecewise-flat simplicial geometrysimplicial Regge-Ricci flow equationsimplicial Ricci flow equation

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Applications of differential geometry to physics (53Z05) Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory (83C27) Polyhedral manifolds (52B70) Triangulating (57R05) Manifolds and cell complexes (57-XX)

Related Items

Book Review: Ricci flow for shape analysis and surface registration: theories, algorithms and applications, On combinatorial Calabi flow with hyperbolic circle patterns, Adiabatic isometric mapping algorithm for embedding 2-surfaces in Euclidean 3-space, Super Ricci flows for weighted graphs, A combinatorial Yamabe problem on two and three dimensional manifolds, Topological signals of singularities in Ricci flow, \(\alpha\)-curvatures and \(\alpha\)-flows on low dimensional triangulated manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete quasi-Einstein metrics and combinatorial curvature flows in 3-dimension
• Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds
• Fundamentals of computational conformal geometry
• Bochner's method for cell complexes and combinatorial Ricci curvature
• Discrete Poincaré lemma
• Combinatorial Ricci flows on surfaces.
• Three-manifolds with positive Ricci curvature
• An example of neckpinching for Ricci flow on \(S^{n+1}\)
• Ricci curvature and eigenvalue estimate on locally finite graphs
• The simplicial Ricci tensor
• Formal matched asymptotics for degenerate Ricci flow neckpinches
• Estimating the trace-free Ricci tensor in Ricci flow
• A geometric construction of the Riemann scalar curvature in Regge calculus
• The Hilbert action in Regge calculus
• A fully -dimensional Regge calculus model of the Kasner cosmology
• A Kirchhoff-like conservation law in Regge calculus