Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below

Abstract

In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with $\mathrm{Ric}\ge -ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to the Riemannian manifold of negative curvature. As an application, we construct a Willmore-type inequality for closed hypersurfaces in hyperbolic space and obtain the characterization of geodesic sphere.

18 pages; comments are welcome!