Communications in Analysis and Geometry
Volume 21 (2013)
On the Sacks-Uhlenbeck flow of Riemannian surfaces
Pages: 917 – 955
In this paper, we study an $\alpha$-flow for the Sacks-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map of the $\alpha$-flow is a weak solution to the harmonic map flow. By an application of the $\alpha$-flow, we present a simple proof of an energy identity of a minimizing sequence in each homotopy class.