Rigidity of spacelike hypersurface with constant curvature and intersection angle condition

TL;DR

This paper proves that in Minkowski space, a compact spacelike hypersurface with constant k-th mean curvature and boundary intersection angles must be a hyperboloid or lie in a hyperplane, extending rigidity results.

Contribution

It establishes a new rigidity theorem for spacelike hypersurfaces with boundary under constant curvature and intersection angle conditions.

Findings

Hypersurface must be a hyperboloid or in a hyperplane under given conditions.

Uses auxiliary functions and integral equalities for the proof.

Extends classical rigidity results to hypersurfaces with boundary.

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 $k$-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.