Initial data sets with ends of cylindrical type: II. The vector constraint equation

TL;DR

This paper constructs solutions to the vacuum vector constraint equations on manifolds with cylindrical ends, advancing the understanding of geometric constraints in such settings.

Contribution

It introduces a method for solving the vacuum vector constraint equations specifically on manifolds with cylindrical ends, which was not previously addressed.

Findings

Successfully constructed solutions on cylindrical end manifolds

Extended the class of manifolds where vacuum constraints can be solved

Provided a framework for future research in geometric analysis

Abstract

We construct solutions of the vacuum vector constraint equations on manifolds with cylindrical ends.