Applied Math Seminar- The fractional Yamabe problem and the prescribed scalar curvature problem

Title: The fractional Yamabe problem and the prescribed scalar curvature problem

Speaker: Seunghyeok Kim (Hanyang University, South Korea)
Date and time: Tuesday, January 23, 4-5pm
Place: Monroe 113

 

Abstract: In this talk, we consider two relatively new problems in conformal geometry, namely,  the fractional Yamabe problem and the prescribed fractional scalar curvature problem. They are geometric questions which concern the existence of a metric in a given conformal class  whose associated fractional scalar curvature is constant or a prescribed function. By conformal covariance of the fractional conformal Laplacian, they are reduced to finding positive solutions to nonlocal elliptic equations having nonlinear terms of critical growth. I will first define some geometric objects for which the problems make sense,  and then provide several geometric conditions which ensure the existence of a desired metric. The results for the fractional Yamabe problem were obtained through a collaboration with Monica Musso (PUC, Chile) and Juncheng Wei (UBC, Canada).