# Conformal metrics with constant scalar curvature and constant boundary mean curvature

# Conformal metrics with constant scalar curvature and constant boundary mean curvature

This is a special Geometric Analysis seminar. Please note special day, time and location. Analogous to the Yamabe problem, a very natural question on a compact manifold with boundary is deforming Riemannian metrics to conformal ones with constant scalar curvature and constant mean curvature curvature on the boundary. Escobar proved the existence of such conformal metric when the dimension is 3,4 and 5 or the boundary is not umbilic or the Weyl tensor does not vanish on the boundary. We generalized his result to the case when dimension is 6 and 7. Some other remaining cases left open by Escobar are also considered. I will also introduce the Han-Li conjecture related to this problem. I will show that Han-Li conjecture is true under some conditions. This is a joint work with Professor Xuezhang .