Abstract

In this talk, I will prove a sharp Fenchel-Willmore inequality for closed immersed submanifolds of arbitrary dimension and codimension in a complete Riemannian manifold with non-negative intermediate Ricci curvature. In the hypersurface case, this condition reduces to non-negative Ricci curvature. The result extends relatively recent work of Agostiniani, Fogagnolo, and Mazzieri, as well as classical results of Chen, Fenchel, Willmore, and others. If time permits, I will also present an unexpected connection between this inequality and a logarithmic Sobolev inequality on submanifolds. This is joint work with Meng Ji.