q-parabolicity of stratified pseudomanifolds and other singular spaces

TL;DR

This paper establishes a sufficient condition for stratified pseudomanifolds with edge metrics to be q-parabolic and explores q-parabolicity in other singular spaces like Hermitian spaces.

Contribution

It introduces a new criterion for q-parabolicity in stratified pseudomanifolds and extends the analysis to other singular spaces such as Hermitian spaces.

Findings

Stratified pseudomanifolds with certain edge metrics are q-parabolic under the new condition.

q-parabolicity also holds for some classes of complex Hermitian spaces.

The paper broadens the understanding of parabolicity in singular geometric spaces.

Abstract

The main result of this paper is a sufficient condition in order to have a compact Thom-Mather stratified pseudomanifold endowed with a $\hat{c}$-iterated edge metric on its regular part $q$-parabolic. Moreover, besides stratified pseudomanifolds, the $q$-parabolicity of other classes of singular spaces, such as compact complex Hermitian spaces, is investigated.