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<p>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 <i>k</i>-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.</p>

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Rigidity of spacelike hypersurface with constant curvature and intersection angle condition

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Shanze Gao

摘要

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 k-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.