Energy identity for a sequence of Sacks-Uhlenbeck maps to a sphere

Series: 
PDE Seminar
Friday, February 10, 2017 - 14:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of Science and Technology of China
,  
Organizer: 
For a map u from a Riemann surface M to a Riemannian manifold and a>1, the a-energy functional is defined as E_a(u)=\int_M |\nabla u|^{2a}dx. We call u_a a sequence of Sacks-Uhlenbeck maps if u_a is a critical point of E_a, and sup_{a>1} E_a(u_a)<\infty. In this talk, when the target manifold is a standard sphere S^K, we prove the energy identity for a sequence of Sacks-Uhlenbeck maps during blowing up.