On the Sacks-Uhlenbeck flow of Riemannian surfaces

In this paper, we study an $α$-flow for the Sack-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map by the $α$-flows 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.

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