Title:  The singular Yamabe problem for Sobalev-regular metrics

Abstract: This talk concerns complete, conformally-compact manifolds whose local geometry approaches that of hyperbolic space near the conformal boundary. We work with Sobolev-regular metrics that are locally continuous and develop Fredholm theory for corresponding elliptic geometric operators. As an application, we show that the Yamabe problem is well posed within the regularity classes of metrics that we define.

This work was done jointly with David Maxwell (UAF) and John M Lee (UW).