ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 35, 58 Han, Zheng-Chao, Rutgers University, USA New existence results on conformal metrics with constant interior scalar curvature and constant boundary mean curvature Let (M^{n}, g_{0}) be a compact Riemannian manifold with boundary ∂M. We consider the problem of looking for a metric g on M conformal to g_{0} and having constant scalar curvature c_{1} on M and constant mean curvature c_{2} on ∂M. This is a generalization of the Yamabe problem to manifolds with boundary. Previous results related to this problem were obtained by J. Escobar in the case c_{2} = 0 and c_{1} appropriately normalized, or in the case c_{1} = 0 and c_{2} appropriately normalized. We present new results on the existence and apriori estimates of such metrics on almost all manifolds for any prescribed c_{2}(after c_{1} has been appropriately normalized). This is joint work with Yanyan Li.