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| Proper Submanifolds in Product Manifolds |
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Citation： |
Hongbing QIU,Yuanlong XIN.Proper Submanifolds in Product Manifolds[J].Chinese Annals of Mathematics B,2012,33(1):1~16 |
| Page view： 3523
Net amount： 2713 |
Authors： |
Hongbing QIU; Yuanlong XIN; |
Foundation： |
the National Natural Science Foundation of China (No. 10971028). |
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| Abstract： |
The authors obtain various versions of the Omori-Yau’s maximum principleon complete properly immersed submanifolds with controlled mean curvature in certainproduct manifolds, in complete Riemannian manifolds whose k-Ricci curvature has strongquadratic decay, and also obtain a maximum principle for mean curvature flow of completemanifolds with bounded mean curvature. Using the generalized maximum principle, anestimate on the mean curvature of properly immersed submanifolds with bounded projectionin N1 in the product manifold N1 ×N2 is given. Other applications of the generalizedmaximum principle are also given. |
Keywords： |
Calabi-Chern problem, Omori-Yau maximum principle, Properly immersed submanifold, Mean curvature flow, Stochastic completeness |
Classification： |
53C40,35B50 |
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