Seminar Analysis: Yannick Sire (University of Marseille)

The fractional Yamabe problem

In the last years, a substantial amount of work has been devoted to understand elliptic, parabolic and hyperbolic problems with non local diffusion. In this talk, I will introduce a new class of conformally covariant operators of fractional order generalizing the scalar and Paneitz curvature. I will describe the associated Yamabe problem, in the regular and singular settings. I will give some existence results and discuss open problems.

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