Analysis Seminar

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Singular Sphere Covering Inequality and Liouville-type problems

Speaker: Changfeng Gui, University of Texas at San Antonio

Location: Warren Weaver Hall 317

Date: Monday, December 3, 2018, 12:50 p.m.

Synopsis:

In this talk, I will present a singular version of the Sphere Covering Inequality and its applications to the study of singular Liouville-type problems with super harmonic weights. In particular, new uniqueness results for solutions of the singular mean field equation on spheres as well as in bounded domains will be discussed. This approach  also gives a new self-contained proofs of previously known results, such as the uniqueness of spherical convex polytopes first established by Luo and Tian. I will also show new symmetry results for the spherical Onsager vortex equation.