Mean exit times from submanifolds with bounded mean curvature

2023/07/19 by G. Pacelli Bessa, Bessa, G. Pacelli, Steen Markvorsen +3
Mathematics · #58J65 #60J65 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Primary 53C42 #Secondary 58C40

paper · pdf · doi:10.48550/arxiv.2307.09716

openalex publication_date 2023/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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