Title: Some geometrical problems for the conformal fractional Laplacian

Speaker: Prof. Maria Gonzalez（Universitat Politecnica de Catalunya, Spain)

Time: 3:30-4:30pm, July 26, 2010

Venue: Room 1328 at BICMR (北京大学资源大厦1328教室）

Abstract:I will present some geometric results involving the fractional Laplacian. Although it is a non-local, fractional order operator, it can be characterized as a local operator in a manifold of one more dimension by means of a degenerate elliptic equation. In particular, I will concentrate on the fractional conformal Laplacian and its associated curvature.

On the Yamabe problem: I settled down the conformal invariance question (or the dependence of the background metric in the extension), and I corrected some errors in the last proof, so I believe it is in a pretty decent shape. Let me try to finish as much as I can before the trip.