Mean Exit Times from Submanifolds with Bounded Mean Curvature

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-07-22 DOI:10.1007/s11118-024-10160-6

G. Pacelli Bessa, Steen Markvorsen, Leandro F. Pessoa

引用次数: 0

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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有界平均曲率子曼形体的平均出口时间

我们证明，具有无限平均退出时间的子漫游无法等轴地、最小地浸入某些积空间的圆柱体、角柱体、圆锥体和楔形中。我们的方法不是基于无穷大时的弱最大原则，因此它允许我们概括以前关于随机完全子曲面不可浸没性的结果。我们还得出了浸入圆柱体的具有小平均曲率的子满足矩塔的估计值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.