Rigidity of spacelike hypersurface with constant curvature and intersection angle condition
Differential Geometry
2026-03-17 v4
Abstract
In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its -th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. The proof is based on an auxiliary function and associated integral equality.
Keywords
Cite
@article{arxiv.2412.17410,
title = {Rigidity of spacelike hypersurface with constant curvature and intersection angle condition},
author = {Shanze Gao},
journal= {arXiv preprint arXiv:2412.17410},
year = {2026}
}
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