Communications in Analysis and Geometry

Volume 21 (2013)

Number 5

On the Sacks-Uhlenbeck flow of Riemannian surfaces

Pages: 917 – 955



Min-Chun Hong (Department of Mathematics, The University of Queensland, Brisbane, Australia)

Hao Yin (School of Mathematical Sciences, University of Science and Technology of China, Hefei, China)


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.

Published 27 December 2013