A curvature estimate for stable marginally outer trapped hypersurface with a free boundary

Abstract

A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a uniform area bound. Our proof is based on an iteration argument. The curvature estimate was previously known via a blowup argument for stable minimal hypersurfaces.

arXiv comment19 pages; comments wellcome; second version corrected some computation mistakes