Sharp sobolev inequalities in global analysis
OCT 24, 2013 | 2:00 PM TO 4:00 PM
The Graduate Center
365 Fifth Avenue
October 24, 2013: 2:00 PM-4:00 PM
Initiative for the Theoretical Sciences (ITS) sponsored Applied Mathematics Nonlinear Analysis Seminar
"Sharp Sobolev inequalities in global analysis"
Speaker: Meijun Zhu (Univ. of Oklahoma)
Abstract: In this talk, I shall explain how PDEs can be used for the study of global analysis problems, in particular the essential roles that certain sharp Sobolev inequalities play: From the uniformization Theorem, one can obtain Gauss-Bonnet formula; From the sharp Sobolev inequality, one can solve the Yamabe problem under the energy condition; Using the fact that Liouville energy is bounded from below, one can reprove the unifromization theorem via Ricci flow on a topological sphere. Sharp Sobolev inequality with negative power will also be discussed.