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Fractional Laplacians and extension problems: the higher rank case (Joint with Maria del Mar Gonzalez):

Banff International Research Station for Mathematical Innovation and Discovery

The aim of this talk is to define conformal operators that arise from an extension problem of co-dimension two. To this end we interpret and extend results of representation theory from a purely analytic point of view. In the first part of the talk I will give definitions and interpretations of the fractional Laplacian and the conformal fractional Laplacian in the general framework of representation theory on symmetric spaces and also from the point of view of scattering operators in conformal geometry. In the second part of the talk I will show constructions of boundary operators with good conformal properties that generalise the fractional Laplacian in $\mathbb R^n$ using an extension problem in which the boundary is of co-dimension two. Then we extend these results to more general manifolds that are not necessarily symmetric space

Mathematics; Partial differential equations; Differential geometry

video/mp4

Author affiliation: Pontificia Universidad Catolica de Chile

2017-11-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63642

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/