Geometry of compact quasi-Einstein manifolds with boundary

TL;DR

This paper investigates the geometry of compact quasi-Einstein manifolds with boundary, providing sharp boundary estimates, a characterization theorem based on boundary surface gravity, and a boundary estimate involving Brown-York mass.

Contribution

It introduces new sharp boundary estimates and a characterization theorem for quasi-Einstein manifolds, advancing understanding of their geometric properties.

Findings

Established sharp boundary estimates for quasi-Einstein manifolds.

Derived a characterization theorem using boundary surface gravity.

Proved a boundary estimate involving Brown-York mass.

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.