On the Sacks-Uhlenbeck flow of Riemannian surfaces

2010/07/19 by Min-Chun Hong, Hao Yin, Hong, Min-Chun +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1007.3052

Abstract

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.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

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