Compact quasi-Einstein manifolds with boundary

TL;DR

This paper investigates compact quasi-Einstein manifolds with boundary, establishing boundary estimates and characterizing those with connected boundary under pinching conditions as isometric to the standard hemisphere.

Contribution

It provides boundary estimates for compact quasi-Einstein manifolds and characterizes those with connected boundary satisfying pinching conditions as standard hemispheres.

Findings

Boundary estimates similar to static and V-static spaces.

Connected boundary manifolds under pinching are isometric to the hemisphere.

Extension of geometric analysis to quasi-Einstein manifolds.

Abstract

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we show that compact quasi-Einstein manifolds with connected boundary and satisfying a suitable pinching condition must be isometric, up to scaling, to the standard hemisphere $\mathbb{S}_{+}^{n}.$