A class of solutions to the conformal constraint equations on compact manifolds with apparent horizon boundary conditions

TL;DR

This paper develops solutions to Einstein's constraint equations on compact manifolds with apparent horizon boundaries, focusing on low regularity conditions to broaden applicability in geometric analysis and general relativity.

Contribution

It introduces a novel approach to solving conformal constraint equations with low regularity assumptions on manifolds with apparent horizon boundaries.

Findings

Established existence of solutions under low regularity conditions

Extended the class of boundary conditions for Einstein constraints

Provided new analytical techniques for geometric PDEs

Abstract

This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.