On the Sacks-Uhlenbeck flow of Riemannian surfaces

Details On the Sacks-Uhlenbeck flow of Riemannian surfaces On the Sacks-Uhlenbeck flow of Riemannian surfaces

2010-07-19

arxiv.org/abs/1007.3052v2

Mathematics

Analysis of PDEs

minor changes

Scientific paper

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

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