# Analysis Seminar

#### A Fractional Yamabe Flow and Some Applications

Speaker: Tianling Jin, Rutgers University

Location: Warren Weaver Hall 1302

Date: Thursday, January 19, 2012, 11 a.m.

Synopsis:

In this talk, we introduce a fractional Yamabe flow involving nonlocal conformally invariant operators on the conformal infinity of asymptotically hyperbolic manifolds, and show that on the conformal spheres $$(S^n, [g_{S^n}])$$, it converges to the standard sphere up to a Mobius diffeomorphism. This result allows us to obtain extinction profiles of solutions of some fractional porous medium equations. In the end, we use this fractional fast diffusion equation, together with its extinction profile and some estimates of its extinction time, to improve a Sobolev inequality via a quantitative estimate of the remainder term. This is joint work with Jingang Xiong.