Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (2): 474-483.doi: 10.1007/s10473-024-0206-z

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A STABILITY RESULT FOR TRANSLATING SPACELIKE GRAPHS IN LORENTZ MANIFOLDS

Ya GAO, Jing MAO*, Chuanxi WU   

  1. 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).

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.

CLC Number: 

  • 53C20
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