On p-Parabolicity of Riemannian Submersions

TL;DR

This paper establishes criteria for p-parabolicity in Riemannian submersions, showing how properties of the base and fiber influence the total space, with specific results for warped manifolds based on volume growth.

Contribution

It provides new conditions linking p-parabolicity of the base and total space in Riemannian submersions, including volume bounds and growth criteria for warped manifolds.

Findings

If the base is p-parabolic and fibers have bounded volume, then the total space is p-parabolic.

Characterization of p-parabolicity in warped manifolds via volume growth conditions.

Abstract

We provide some criteria to $p$-parabolicity of Riemannian submersions. In particular, if $N$ is $p$-parabolic and $\pi:M\to N$ is a Riemannian submersion with uniformly bounded volume of fibers, then $M$ is also $p$-parabolic. In the case of warped manifolds we characterize $p$-parabolicity in terms of a volume growth condition.