On stochastically complete submanifolds
Differential Geometry
2011-01-21 v2
Abstract
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.
Cite
@article{arxiv.1012.4439,
title = {On stochastically complete submanifolds},
author = {G. Pacelli Bessa and Luquesio P. Jorge},
journal= {arXiv preprint arXiv:1012.4439},
year = {2011}
}
Comments
This paper has been withdrawn by the authors. The theorem that we seemed to prove is false. There are stochastically incomplete properly immersed in $\mathbb{R}^{n}$