Complete Conformal Metrics of Negative Ricci Curvature on Compact Riemannian Manifolds with Boundary

GUEST LECTURE IN GEOMETRIC PDE
Topic:Complete Conformal Metrics of Negative Ricci Curvature on Compact Riemannian Manifolds with Boundary
Speaker:Bo Guan
Affiliation:Ohio State University
Date:Tuesday, November 4
Time/Room:1:30pm - 2:30pm/S-101

We consider the problem of finding complete conformal metrics determined by a symmetric function of Ricci tensor in a negative convex cone on compact manifolds. A consequence of our main results is that any smooth bounded domain in Euclidean space of dimension greater or equal to 3 admits a complete conformally flat metric of negative Ricci curvature with the $\det (- Ric) = 1$.