Regularity of the boundary of the trapped region in asymptotically Euclidean Riemannian manifolds of arbitrarily large dimensions

TL;DR

This paper proves that in high-dimensional asymptotically Euclidean Riemannian manifolds, the boundary of the trapped region is mostly a smooth minimal hypersurface with singularities of high codimension.

Contribution

It establishes regularity and stability properties of the trapped region boundary in high-dimensional asymptotically Euclidean manifolds.

Findings

Boundary is a stable smooth minimal hypersurface

Singular set has codimension at least 8

Results hold for dimensions ≥ 3

Abstract

We prove that the boundary of the trapped region in an asymptotically Euclidean Riemannian manifold of dimension at least 3 is a stable smooth minimal hypersurface except for a singular set of codimension at least 8.