A fractional Yamabe flow and some applications

Details A fractional Yamabe flow and some applications A fractional Yamabe flow and some applications

2011-10-25

arxiv.org/abs/1110.5664v1

Mathematics

Analysis of PDEs

44 pages

Scientific paper

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 $(\Sn, [g_{\Sn}])$, it converges to the standard sphere up to a M\"obius 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.

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