Geometry of compact quasi-Einstein manifolds with boundary

Abstract

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a characterization theorem for such manifolds in terms of the surface gravity of the boundary components, which leads to a new sharp geometric inequality. In addition, we prove a boundary estimate for compact quasi-Einstein manifolds with (possibly disconnected) boundary in terms of the Brown–York mass.