Results 1 to 10 of about 709 (127)
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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Deep learning as Ricci flow. [PDF]
Sci RepAbstract Deep 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. While some progress has been made toward understanding these transformations in neural networks with smooth ...
Baptista A +5 more
europepmc +6 more sources
Pluripotential Kähler–Ricci flows [PDF]
Geometry & Topology, 2020 We develop a parabolic pluripotential theory on compact K{ }hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{ }re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ }hler-Ricci flow on varieties with log terminal singularities.
Guedj, Vincent +2 more
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Diameter Estimate in Geometric Flows
Mathematics, 2023 We prove the upper and lower bounds of the diameter of a compact manifold (M,g(t)) with dimRM=n(n≥3) and a family of Riemannian metrics g(t) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow,
Shouwen Fang, Tao Zheng
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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.
Miller, Warner A. +4 more
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Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows [PDF]
Geometry & Topology, 2021 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.
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Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes
Journal of High Energy Physics, 2023 Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field.
Davide De Biasio +3 more
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The Ricci–Bourguignon flow [PDF]
Pacific Journal of Mathematics, 2017 Minor ...
GIOVANNI CATINO +4 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.
Valentino Tosatti, Ben Weinkove
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