Complete CMC hypersurfaces in Minkowski (n+1)-space
Differential Geometry
2024-10-25 v1 General Relativity and Quantum Cosmology
Geometric Topology
Abstract
We prove that any regular domain in Minkowski space is uniquely foliated by spacelike constant mean curvature (CMC) hypersurfaces. This completes the classification of entire spacelike CMC hypersurfaces in Minkowski space initiated by Choi and Treibergs. As an application, we prove that any entire surface of constant Gaussian curvature in 2+1 dimensions is isometric to a straight convex domain in the hyperbolic plane.
Cite
@article{arxiv.1912.05477,
title = {Complete CMC hypersurfaces in Minkowski (n+1)-space},
author = {Francesco Bonsante and Andrea Seppi and Peter Smillie},
journal= {arXiv preprint arXiv:1912.05477},
year = {2024}
}
Comments
31 pages, 3 figures