Hypersurfaces of prescribed null expansion

TL;DR

This paper investigates hypersurfaces with specific null expansion properties in initial data sets, introducing a stability concept, proving a topology theorem, and adapting existing methods to establish existence results.

Contribution

It introduces a new notion of stability for hypersurfaces with prescribed null expansion and adapts Perron's method for existence proofs in this context.

Findings

Established a stability notion for hypersurfaces with prescribed null expansion.

Proved a topology theorem related to these hypersurfaces.

Adapted Eichmair's Perron approach to this setting.

Abstract

We study hypersurfaces with prescribed null expansion in an initial data set. We propose a notion of stability and prove a topology theorem. Eichmair's Perron approach toward the existence of marginally outer trapped surface adapts to the settings of hypersurfaces with prescribed null expansion with only minor modifications.