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arXiv · 1802.04244

Uniqueness of isometric immersions with the same mean curvature

Chunhe Li·Pengzi Miao·Zhizhang Wang
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Abstract

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also give similar results if the mean curvature condition is replaced by an $σ_2$-curvature condition.

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Chunhe Li, Pengzi Miao, Zhizhang Wang. 2018-04-16. Uniqueness of isometric immersions with the same mean curvature. https://arxiv.org/abs/1802.04244

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