Geometric inequalities for critical metrics of the volume functional

Abstract

In this article, we investigate the geometry of critical metrics of the volume functional on an $n$-dimensional compact manifold with (possibly disconnected) boundary. We establish sharp estimates to the mean curvature and area of the boundary components of critical metrics of the volume functional on a compact manifold. In addition, localized version estimates to the mean curvature and area of the boundary of critical metrics are also obtained.

To appear in Annali di Matematica Pura ed Applicata

References in corpus (2)

• On the mass of static metrics with positive cosmological constant - I
• On the uniqueness of Schwarzschild-de Sitter spacetime