Mean time exit and isoperimetric inequalities \\for minimal submanifolds of $N\times \mathbb{R}$

TL;DR

This paper improves isoperimetric inequalities and mean exit time estimates for minimal submanifolds in product spaces and Hadamard spaces, advancing geometric analysis in these contexts.

Contribution

It establishes sharper isoperimetric inequalities and mean time exit bounds for minimal submanifolds of $N\times\mathbb{R}$ and Hadamard spaces with tamed second fundamental form.

Findings

Enhanced isoperimetric inequalities for minimal submanifolds in product spaces.

Improved mean exit time estimates for these submanifolds.

New isoperimetric inequalities for submanifolds in Hadamard spaces.

Abstract

Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal submanifolds of $N\times\mathbb{R}$. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form.