The Plateau problem for marginally outer trapped surfaces

TL;DR

This paper addresses the existence of marginally outer trapped surfaces in general Cauchy data sets by solving a Plateau problem using advanced geometric measure theory techniques, providing new insights and adaptable methods.

Contribution

It introduces a novel approach to the Plateau problem for marginally outer trapped surfaces employing the Perron method and geometric measure theory, with broader applicability to non-variational problems.

Findings

Successfully solves the Plateau problem for marginally outer trapped surfaces.

Develops new geometric insights into properties of these surfaces.

Creates flexible techniques adaptable to other existence problems.

Abstract

We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of Jang's equation. Substantial new geometric insights regarding the lower order properties of marginally outer trapped surfaces are gained in the process. The techniques developed in this paper are flexible and can be adapted to other non-variational existence problems.