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 an integral curvature estimate involving the Yamabe constant, which allows us to get an obstruction result to the existence of new examples.