Results 1 to 10 of about 4,657,305 (302)
Deep learning as Ricci flow [PDF]
Scientific ReportsDeep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications.
Anthony Baptista +5 more
doaj +6 more sources
Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency. [PDF]
Calc Var Partial Differ Equ, 2023 We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow.
Li X, Zhang QS.
europepmc +3 more sources
Yamabe constant evolution and monotonicity along the conformal Ricci flow
AIMS Mathematics, 2022 We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric g(t), t∈[0,T), the time evolution formula for the Yamabe constant Y(g(t)) is derived.
Yanlin Li +3 more
doaj +2 more sources
Rendiconti Lincei, Matematica e Applicazioni, 2021 We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
Valentino Tosatti, B. Weinkove
semanticscholar +3 more sources
Cobordism, singularities and the Ricci flow conjecture [PDF]
Journal of High Energy Physics, 2023 In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented.
David Martín Velázquez +2 more
doaj +2 more sources
Community Detection on Networks with Ricci Flow. [PDF]
Sci Rep, 2019 Many complex networks in the real world have community structures – groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.
Ni CC, Lin YY, Luo F, Gao J.
europepmc +3 more sources
Advances in Nonlinear Analysis, 2023 In the present work, we find the Lie point symmetries of the Ricci flow on an n-dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics.
López Enrique +2 more
doaj +3 more sources
Ricci flow on Kähler manifolds [PDF]
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001 In this paper, we announce the following results: Let M be a Kaehler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature and positive at least at one point, then the K hler-Ricci flow converges exponentially fast to a Kaehler-Einstein metric with constant bisectional curvature.
Xiuxiong Chen, Gang Tian
openalex +5 more sources
Communications in Mathematical Physics, 2014 We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the discrete formulation of Einstein's theory of general relativity known as Regge calculus.
Warner A. Miller +5 more
openaire +5 more sources
High genus surface parameterization using the Euclidean Ricci flow method [PDF]
Scientific ReportsThe parameterization of surfaces, which is related to many frontier problems in mathematics, has long been a challenge for scientists and engineers.
Yuan-guang Wang
doaj +2 more sources