Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, January 14, 2019 - 12:00 to 12:50

Location:

Kidd 237

Guest Speaker:

Institution:

Lewis & Clark College

Abstract:

Given a conformally compact Riemannian manifold, the singular Yamabe problem seeks to find a conformally related geometry with constant scalar curvature. Results of Andersson, Chrusciel, and Friedrich show that even if the original geometry has a smooth conformal compactification, the conformally related metric might exhibit singular behavior at conformal infinity. In this talk I present a framework, developed jointly with Isenberg, Lee, and Stavrov, in which solving the Yamabe problem is "closed' in the sense that solutions lie in the same regularity class as the original metric. This framework has further applications to geometric analysis problems in general relativity, which I discuss as time permits.