The Yamabe problem for the conformal fractional Laplacian

The Yamabe problem for the conformal fractional Laplacian

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Maria del Mar Gonzalez, Universitat Politècnica de Catalunya
Fine Hall 314

Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf type maximum principle together with interplays between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extend the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem. This is joint work with J. Qing.