Asymptotic Curvature Bounds for Conformally Flat Metrics on the Plane

Miodrag Mateljević, Ivan Anić, Stephen Taylor

The decay rate of the Gauss curvature of conformally flat planer surfaces of strictly negative curvature is studied. It is shown that generically there is an asymptotic sequence that decays faster than quadratically in the distance from the origin. In the case that the conformal factor is of finite order, it is shown that one can improve this decay rate.