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Sharp sobolev inequalities in global analysis

OCT 24, 2013 | 2:00 PM TO 4:00 PM

Details

WHERE:

The Graduate Center
365 Fifth Avenue

ROOM:

5417

WHEN:

October 24, 2013: 2:00 PM-4:00 PM

ADMISSION:

Free

Description

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.