The decay rate of the Gauss curvature of conformally flat planer surfaces of strictly negative curvature is studied. It is show 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.
All Science Journal Classification (ASJC) codes
- Conformally Flat Surfaces
- Gauss Curvature Decay
- Liouville Equa- tion