On the Sacks-Uhlenbeck flow of Riemannian surfaces

Abstract

In this paper, we study an α-flow for the Sacks-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map of the α-flow is a weak solution to the harmonic map flow. By an application of the α-flow, we present a simple proof of an energy identity of a minimizing sequence in each homotopy class.