A fractional Yamabe flow and some applications

Abstract

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 Möbius 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.

final version, to appear in J. Reine Angew. Math

References in corpus (3)

• On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
• Asymptotics of the fast diffusion equation via entropy estimates
• Hydrodynamic limit of particle systems with long jumps

Cited by in corpus (1)

• Remainder terms in the fractional Sobolev inequality