Results 1 to 10 of about 4,623,808 (311)
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 +4 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
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
Stability and instability of Ricci solitons [PDF]
Calc. Var. Partial Differ. Equ. 53 no. 1-2, pp. 265-287 (2015), 2014 We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $(M,g)$ is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton.
Kroencke, Klaus
arxiv +4 more sources
Producing 3d Ricci flows with non-negative Ricci curvature via singular Ricci flows [PDF]
Geom. Topol. 25 (2021) 3629-3690, 2020 We extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d complete Riemannian manifold with non-negative Ricci curvature, there exists a smooth Ricci flow starting from it.
arxiv +4 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 +4 more sources
Singularities of Connection Ricci Flow and Ricci Harmonic Flow [PDF]
arXiv, 2013 In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specifically, we give the definition of three types of singularities and their corresponding singularity models, and then prove the convergence. In addition, for Ricci harmonic flow, we
arxiv +3 more sources
Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
doaj +2 more sources