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

TL;DR

This paper establishes a curvature estimate for stable marginally outer trapped hypersurfaces with free boundaries, extending known results from minimal hypersurfaces using an iteration argument.

Contribution

It provides a new curvature estimate for stable marginally outer trapped hypersurfaces with free boundary conditions, using a different proof technique from previous blowup methods.

Findings

Curvature estimate proven for stable marginally outer trapped hypersurfaces

Extension of minimal hypersurface results to general relativity contexts

Proof based on an iteration argument rather than blowup analysis

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.