A Rigidity theorem on conformally compact Einstein manifolds in high dimensions

TL;DR

This paper proves a rigidity theorem for high-dimensional conformally compact Einstein manifolds, extending previous results from four dimensions to five or more, highlighting the uniqueness of such geometric structures.

Contribution

It extends a Liouville type rigidity result for asymptotically hyperbolic Einstein metrics from 4D to higher dimensions (d ≥ 5).

Findings

Rigidity theorem established for d ≥ 5.

Extension of previous 4D results to higher dimensions.

Highlights uniqueness of conformally compact Einstein manifolds in high dimensions.

Abstract

In this paper, we establish a Liouville type rigidity result for a class of asymptotically hyperbolic non-compact Einstein metrics defined on manifolds of dimension $d\ge 5$ extending the earlier result in dimension $d=4$.