Compact quasi‐Einstein manifolds with boundary

Abstract

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds similar 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 𝕊 𝑛 + .