Results 1 to 10 of about 8,322 (165)
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
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The Soliton-Ricci Flow with variable volume forms
Complex Manifolds, 2016 We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the ...
Pali Nefton
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The spinorial energy for asymptotically Euclidean Ricci flow [PDF]
Advanced Nonlinear Studies, 2023 This article introduces a functional generalizing Perelman’s weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well defined on a wide class of noncompact manifolds; on asymptotically Euclidean manifolds, the functional is shown
Baldauf Julius, Ozuch Tristan
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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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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
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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
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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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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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The ∗-Ricci Operator on Hopf Real Hypersurfaces in the Complex Quadric
Mathematics, 2022 We study the ∗-Ricci operator on Hopf real hypersurfaces in the complex quadric. We prove that for Hopf real hypersurfaces in the complex quadric, the ∗-Ricci tensor is symmetric if and only if the unit normal vector field is singular.
Rongsheng Ma, Donghe Pei
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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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