Abstract:
The purpose of this talk is to provide a unified perspective on a broad family of monotonicity formulas in geometric analysis. One outcome of these monotonicities is the Willmore inequality on Riemannian manifolds with nonnegative Ricci curvature. Additionally, a related, though less direct, consequence is (a weaker version of) Hamilton’s pinching conjecture: a complete, connected, noncompact Riemannian 3-manifold with superquadratic volume growth that satisfies the Ricci-pinching condition must be flat.
Based on joint work with Luca Benatti and Marco Pozzetta.