On stochastically complete submanifolds

Details On stochastically complete submanifolds On stochastically complete submanifolds

2010-12-20

arxiv.org/abs/1012.4439v2

Mathematics

Differential Geometry

This paper has been withdrawn by the authors. The theorem that we seemed to prove is false. There are stochastically incomplet

Scientific paper

Using a deep criteria due to Pigola, Rigoli and Setti, we prove that a geodesically complete, properly immersed submanifold M of a stochastically complete Riemannian manifold N is stochastically complete. This implies that the weak Omori-Yau maximum principle holds on M. As geometric application, we prove sectional curvature estimates for properly immersed cilindrically bounded submanifolds.

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