超弹性Ricci流:梯度流、局部存在唯一性和Perelman能量泛函

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED Quarterly of Applied Mathematics Pub Date : 2023-02-08 DOI:10.1090/qam/1643

M. Slemrod

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引用次数: 0

摘要

超弹性Ricci流方程通过增加Cauchy应力张量来修正经典Ricci流，Cauchy张量本身是由自由能导出的。本文证明了超弹性Ricci流具有G.Perelman对经典Ricci流导出的三个性质，特别是它微分等价于梯度流，在时间上局部存在唯一的光滑解，系统具有不递减的能量函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hyper-elastic Ricci flow: Gradient flow, local existence-uniqueness, and a Perelman energy functional

The equation of hyper-elastic Ricci flow amends classical Ricci flow by the addition of the Cauchy stress tensor which itself is derived from the a free energy. In this paper hyper-elastic Ricci flow is shown to possess three properties derived by G. Perelman for classical Ricci flow, specifically it is diffeomorphically equivalent to a gradient flow, unique smooth solutions exist locally in time, and the system possesses a non-decreasing energy function.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.