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arXiv · 2307.09716

Mean exit times from submanifolds with bounded mean curvature

G. Pacelli Bessa·Steen Markvorsen·Leandro F. Pessoa
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Abstract

We show that submanifolds with infinite mean exit time can not be isometrically and minimally immersed into cylinders, horocylinders, cones, and wedges of some product spaces. Our approach is not based on the weak maximum principle at infinity, and thus it permits us to generalize previous results concerning non-immersibility of stochastically complete submanifolds. We also produce estimates for the complete tower of moments for submanifolds with small mean curvature immersed into cylinders.

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G. Pacelli Bessa, Steen Markvorsen, Leandro F. Pessoa. 2023-07-20. Mean exit times from submanifolds with bounded mean curvature. https://arxiv.org/abs/2307.09716

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