Recent Progress on the Fractional Yamabe Problem.

Abstract: Let $(M^n, [\hat{g}])$ be the conformal infinity of an asymptotically hyperbolic Einstein (AHE) manifold $(X^{n+1},g^+).$ We will take the scattering operator associated to the AHE filling in as the fractional conformal Laplacian. Equipped with fractional conformal Laplacians defined via the AHE manifold, we can define a fractional Yamabe problem, looking for a conformal metric of $(M^n,[\hat{g}])$ which has constant fractional scalar curvature. We will present some new developments on the fractional Yamabe problem assuming an AHE filling in.

Posted on Nov 29, 2024 in Differential Equations, Seminars