A functional inequality on the boundary of static manifolds

Abstract

On the boundary of a compact Riemannian manifold $(\Omega ,g)$ whose metric $g$ is static, we establish a functional inequality involving the static potential of $(\Omega ,g)$, the second fundamental form and the mean curvature of the boundary $\partial \Omega$ respectively.

11 pages; to appear in Asian J. Math

References in corpus (4)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Global and uniqueness properties of stationary and static spacetimes with outer trapped surfaces
• Boundary Effect of Ricci Curvature