#### Event Details

Título Conferencia: ODE solutions for the fractional Laplacian equations arising in conformal geometry

Conferenciante: Azahara de la Torre (Universidad Politécnica de Cataluña)

Abstract: We construct some ODE solutions for the fractional Yamabe problem in conformal geometry. The fractional curvature, a generalization of the usual scalar curvature, is defined from the conformal fractional Laplacian, which is a non-local operator constructed on the conformal infinity of a conformally compact Einstein manifold. These ODE solutions are a generalization of the usual Delaunay and, in particular, solve the fractional Yamabe problem with an isolated singularity at the origin \[ (−\Delta )^γu=c_{n,γ}u^{\frac{n+2γ}{n−2γ}}, \qquad u\geq 0. \] This is a fractional order ODE for which new tools need to be developed. The key of the proof is the computation of the fractional Laplacian in polar coordinates.

Conferenciante: Azahara de la Torre (Universidad Politécnica de Cataluña)

Abstract: We construct some ODE solutions for the fractional Yamabe problem in conformal geometry. The fractional curvature, a generalization of the usual scalar curvature, is defined from the conformal fractional Laplacian, which is a non-local operator constructed on the conformal infinity of a conformally compact Einstein manifold. These ODE solutions are a generalization of the usual Delaunay and, in particular, solve the fractional Yamabe problem with an isolated singularity at the origin \[ (−\Delta )^γu=c_{n,γ}u^{\frac{n+2γ}{n−2γ}}, \qquad u\geq 0. \] This is a fractional order ODE for which new tools need to be developed. The key of the proof is the computation of the fractional Laplacian in polar coordinates.