Calculus of Variations and Geometric Measure Theory

The Sacks-Uhlenbeck flow on Riemannian surfaces and its applications

Min-Chun Hong (University of Queensland, Australia)

created by magnani on 22 Apr 2011

27 apr 2011


Dipartimento di Matematica - Sala Seminari - ore 17:00

ABSTRACT: In their well-known paper (Ann. Math. 1981), Sacks and Uhlenbeck proposed a family of the perturbed functional (now called the Sacks and Uhlenbeck functional) to establish many existence results of minimizers in a given homotopy class of maps. In this talk, we study an alpha-flow for the Sacks-Uhlenbeck functional on Riemannian surfaces and prove that the limiting map by 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.