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A stability result for translating spacelike graphs in Lorentz manifolds

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Abstract

In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ Mn in the Lorentz manifold Mn × ℝ with the metric −ds2 + σ, where Mn is a complete Riemannian n-manifold with the metric σ, Ω has piecewise smooth boundary, and ℝ denotes the Euclidean 1-space. We prove an interesting stability result for translating spacelike graphs in Mn × ℝ under a conformal transformation.

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Authors and Affiliations

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

    Ya Gao, Jing Mao & Chuanxi Wu

Authors
  1. Ya Gao
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  2. Jing Mao
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  3. Chuanxi Wu
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Corresponding author

Correspondence to Jing Mao.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

This research was supported in part by the NSFC (11801496, 11926352), the Fok Ying-Tung Education Foundation (China), and the Hubei Key Laboratory of Applied Mathematics (Hubei University).

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Gao, Y., Mao, J. & Wu, C. A stability result for translating spacelike graphs in Lorentz manifolds. Acta Math Sci 44, 474–483 (2024). https://doi.org/10.1007/s10473-024-0206-z

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  • DOI: https://doi.org/10.1007/s10473-024-0206-z

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