Results 1 to 10 of about 96,074 (249)
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
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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
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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
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Uniqueness of the Ricci Flow on Complete Noncompact Manifolds [PDF]
, 2005 The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later
Chen, Bing-Long, Zhu, Xi-Ping
core +7 more sources
Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics [PDF]
, 2006 In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions.
Astefanesei D. +8 more
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Hyperbolic Ricci-Bourguignon-Harmonic Flow [PDF]
Mathematics Interdisciplinary Research, 2022 In this paper, we consider hyperbolic Ricci-Bourguignon flow on a compact Riemannian manifold M coupled with the harmonic map flow between M and a fixed manifold N. At the first, we prove the unique short-time existence to solution of this system.
Shahrood Azami
doaj +1 more source
On Weak Super Ricci Flow through Neckpinch
Analysis and Geometry in Metric Spaces, 2021 In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions ...
Lakzian Sajjad, Munn Michael
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The Ricci–Bourguignon flow [PDF]
Pacific Journal of Mathematics, 2017 Minor ...
GIOVANNI CATINO +4 more
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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
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Rendiconti Lincei, Matematica e Applicazioni, 2022 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.
Tosatti, Valentino, Weinkove, Ben
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