Einstein constraints on n dimensional compact manifolds

TL;DR

This paper surveys the solution of Einstein constraint equations on n-dimensional compact manifolds using the conformal method, introducing new results for low regularity solutions and those with unscaled sources.

Contribution

It provides a comprehensive survey and new results on Einstein constraints, especially solutions with low regularity and unscaled sources on compact manifolds.

Findings

New results on solutions with low regularity in $H_{2}$ for n=3

Solutions with unscaled sources analyzed

Enhanced understanding of Einstein constraints on compact manifolds

Abstract

We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions with unscaled sources.