Existence, Regularity, and Properties of Generalized Apparent Horizons

TL;DR

This paper proves the existence and properties of the outermost generalized apparent horizon in initial data sets, confirming a conjecture by Ilmanen and Bray and establishing its outer area minimizing property.

Contribution

It establishes the existence and outer area minimizing nature of the outermost generalized apparent horizon, confirming a conjecture in geometric analysis.

Findings

Proved the existence of the outermost generalized apparent horizon.

Confirmed the horizon is outer area minimizing.

Validated a conjecture by Ilmanen and Bray.

Abstract

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.