Progress on nonuniqueness of solutions to the vacuum Einstein conformal constraint equations with positive Yamabe invariant

TL;DR

This paper generalizes fixed point theorems using half-continuity to enhance understanding of nonuniqueness of solutions in vacuum Einstein conformal equations with positive Yamabe invariant.

Contribution

It introduces a generalized fixed point theorem based on half-continuity and applies it to improve nonuniqueness results for Einstein conformal equations.

Findings

Enhanced nonuniqueness results for vacuum Einstein conformal equations

Application of half-continuity in fixed point theorems

Generalization of classical fixed point theorems

Abstract

In this article, we make a generalization of classical fixed point theorems by using the concept of half-continuity and then apply it to improve the nonuniqueness result for solutions to the vacuum Einstein conformal equations shown by the author in arxiv.org/abs/1507.01081