A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD*

doi:10.1007/s10473-023-0614-5

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2553-2572.doi: 10.1007/s10473-023-0614-5

A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*

Zhengchao JI^1,2

1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China;
2. Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

收稿日期:2022-05-10 修回日期:2023-05-29 发布日期:2023-12-08
作者简介:Zhengchao Ji, E-mail: jizhengchaode@163.com; jizhengchao@zju.edu.cn
基金资助:
The work was supported by the Postdoctoral Fund of Zhejiang Province, China (ZJ2022004).

A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*

Zhengchao JI^1,2

1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China;
2. Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Received:2022-05-10 Revised:2023-05-29 Published:2023-12-08
About author:Zhengchao Ji, E-mail: jizhengchaode@163.com; jizhengchao@zju.edu.cn
Supported by:
The work was supported by the Postdoctoral Fund of Zhejiang Province, China (ZJ2022004).

摘要/Abstract

摘要： In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove that under suitable convex conditions for the initial hypersurface, one can get the long-time existence for the inverse curvature flow. Moreover, we also get that the principal curvatures of the evolving hypersurface converge to $1$ when $t\rightarrow+\infty$.

关键词: star-shaped, quotient curvature, support function

Abstract: In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove that under suitable convex conditions for the initial hypersurface, one can get the long-time existence for the inverse curvature flow. Moreover, we also get that the principal curvatures of the evolving hypersurface converge to $1$ when $t\rightarrow+\infty$.

Key words: star-shaped, quotient curvature, support function

中图分类号:

53C42

Zhengchao JI. A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*[J]. 数学物理学报(英文版), 2023, 43(6): 2553-2572.

Zhengchao JI. A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2553-2572.

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A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*

A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD^*

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