Geometric Analysis and Topology Seminar

I will present integral curvature conditions for a Riemannian metric g on S^4 that quantify the best bilipschitz constant between (S^4,g) and the standard metric on S^4. The condition relies on the integral of the Q-curvature of the metric and the Weyl tensor. This result was originally proven for the case when g=e^{2u}g_c, where g_c is the standard metric on S^4 by Bonk, Heinonen and Saksman. I will show how to extend this result to a larger class of metrics that have a positive Yamabe constant.

This is joint work with Alice Chang and Paul Yang.