Topics in conformally compact Einstein metrics

TL;DR

This paper surveys and presents new results on the existence of conformally compact Einstein metrics with prescribed conformal infinity, addressing key questions in geometric analysis.

Contribution

It offers new insights and open problems in the study of conformally compact Einstein metrics, combining survey and original research.

Findings

Discussion of global existence questions for Einstein metrics

Presentation of new results in conformal geometry

Identification of open problems in the field

Abstract

We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey of this area but also presents new results and a number of open problems.