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.
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
.
DOI: 10.1007/s10473-024-0206-z
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