A note on the p-Parabolicity of Submanifolds

TL;DR

This paper provides a geometric criterion to determine p-parabolicity of certain submanifolds in Riemannian manifolds, focusing on those with controlled second fundamental form for p ≥ 2.

Contribution

It introduces a new geometric criterion for p-parabolicity applicable to submanifolds with bounded second fundamental form.

Findings

Established a criterion for p-parabolicity based on geometric conditions.

Applicable to submanifolds with controlled second fundamental form.

Extends understanding of p-parabolicity in Riemannian geometry.

Abstract

We give a geometric criterion which shows p-parabolicity of a class of submanifolds in a Riemannian manifold, with controlled second fundamental form, for p bigger or equal than 2.