The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose ...The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose k-Ricci curvature has strong quadratic decay, and also obtain a maximum principle for mean curvature flow of complete manifolds with bounded mean curvature. Using the generalized maximum principle, an estimate on the mean curvature of properly immersed submanifolds with bounded projection in N1 in the product manifold N1 x N2 is given. Other applications of the generalized maximum principle are also given.展开更多
基金supported by the National Natural Science Foundation of China (No. 10971028)
文摘The authors obtain various versions of the Omori-Yau＇s maximum principle on complete properly immersed-submanifolds with controlled mean curvature in certain product manifolds, in complete Riemannian manifolds whose k-Ricci curvature has strong quadratic decay, and also obtain a maximum principle for mean curvature flow of complete manifolds with bounded mean curvature. Using the generalized maximum principle, an estimate on the mean curvature of properly immersed submanifolds with bounded projection in N1 in the product manifold N1 x N2 is given. Other applications of the generalized maximum principle are also given.
