The spinorial energy for asymptotically Euclidean Ricci flow

Abstract

This article introduces a functional generalizing Perelman’s weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well defined on a wide class of noncompact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and the Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary.