A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

doi:10.1007/s10473-024-0206-z

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 474-483.doi: 10.1007/s10473-024-0206-z

A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

Ya GAO, Jing MAO^*, Chuanxi WU

Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China

收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2024-04-25 发布日期:2024-04-16
通讯作者: *Jing MAO, E-mail: jiner120@163.com
作者简介:Ya GAO, E-mail: Echo-gaoya@outlook.com; Chuanxi WU, E-mail: cxwu@hubu.edu.cn
基金资助:
NSFC (11801496, 11926352), the Fok Ying-Tung Education Foundation (China), and the Hubei Key Laboratory of Applied Mathematics (Hubei University).

A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

Ya GAO, Jing MAO^*, Chuanxi WU

Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China

Received:2022-11-20 Revised:2023-01-08 Online:2024-04-25 Published:2024-04-16
Contact: *Jing MAO, E-mail: jiner120@163.com
About author:Ya GAO, E-mail: Echo-gaoya@outlook.com; Chuanxi WU, E-mail: cxwu@hubu.edu.cn
Supported by:
NSFC (11801496, 11926352), the Fok Ying-Tung Education Foundation (China), and the Hubei Key Laboratory of Applied Mathematics (Hubei University).

摘要/Abstract

摘要： In this paper, we investigate spacelike graphs defined over a domain $\Omega\subset M^{n}$ in the Lorentz manifold $M^{n}\times\mathbb{R}$ with the metric $-{\rm d}s^{2}+\sigma$, where $M^{n}$ is a complete Riemannian $n$-manifold with the metric $\sigma$, $\Omega$ has piecewise smooth boundary, and $\mathbb{R}$ denotes the Euclidean $1$-space. We prove an interesting stability result for translating spacelike graphs in $M^{n}\times\mathbb{R}$ under a conformal transformation.

关键词: mean curvature flow, spacelike graphs, translating spacelike graphs, maximal spacelike graphs, constant mean curvature, Lorentz manifolds.

Abstract: In this paper, we investigate spacelike graphs defined over a domain $\Omega\subset M^{n}$ in the Lorentz manifold $M^{n}\times\mathbb{R}$ with the metric $-{\rm d}s^{2}+\sigma$, where $M^{n}$ is a complete Riemannian $n$-manifold with the metric $\sigma$, $\Omega$ has piecewise smooth boundary, and $\mathbb{R}$ denotes the Euclidean $1$-space. We prove an interesting stability result for translating spacelike graphs in $M^{n}\times\mathbb{R}$ under a conformal transformation.

Key words: mean curvature flow, spacelike graphs, translating spacelike graphs, maximal spacelike graphs, constant mean curvature, Lorentz manifolds.

中图分类号:

53C20

Ya GAO, Jing MAO, Chuanxi WU. A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS[J]. 数学物理学报(英文版), 2024, 44(2): 474-483.

Ya GAO, Jing MAO, Chuanxi WU. A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS[J]. Acta mathematica scientia,Series B, 2024, 44(2): 474-483.

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A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

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