Title: A geometric approach to fractional powers of the Laplacian and sharp Sobolev trace inequalities

Date: 09/22/2020

Time: 3:00 PM - 4:00 PM

Place: Online (virtual meeting)

A seminal paper of Caffarelli and Silvestre identifies fractional powers of the Laplacian on Euclidean space as Dirichlet-to-Neumann operators. In this talk, I will use conformal geometry to generalize their approach to Riemannian manifolds. More specifically, I will present multiple (equivalent) definitions of (conformally covariant) operators with principal symbol that of a fractional power of the Laplacian. I will also discuss how these operators lead to a simple derivation of a broad family of sharp Sobolev trace inequalities.
https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09