Work

Minimal tubes of the sphere as the dimension grows: Volume and explosion of the mean exit time

Year: 2026

Type: preprint

Abstract: The mean exit time of a Brownian motion from a tube around a closed, minimal embedded \(n\)-dimen\-sional submanifold of the \((n+m)\)-dimen\-sional sphere is studied, establishing two-sided bounds via radial transplant. In accordance with known results when \(n = 0\) or \(m = 1,\) the mean exit time goes to infinity as \(n \to \infty\) and to \(0\) as \(m \to \infty.\) Simultaneously, bounds for the volume of such tubes are derived and compared to Weyl's tube formula.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.08222

Authors: Garcia, Vicent Gimeno i, Torres-Valverde, Martín

Institution: Universitat Jaume I

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Generalitat Valenciana, Universitat Jaume I

OpenAlex ID: W7221009050

Cites:

Cited by:

Related to: 10