$L_{p,q}$-Cohomology of Warped Cylinders

TL;DR

This paper extends existing results on $L_p$-cohomology of warped cylinders to the more general $L_{p,q}$ setting, providing new conditions for nontrivial torsion in surfaces of revolution.

Contribution

It introduces the $L_{p,q}$-cohomology framework for warped cylinders and establishes conditions for nontrivial torsion on surfaces of revolution.

Findings

Extended $L_{p,q}$-cohomology results to warped cylinders.

Derived conditions for nontrivial $L_{p,q}$-torsion on surfaces of revolution.

Connected torsion properties to Hardy constants.

Abstract

We extend some results by Gol'dshtein, Kuz'minov, and Shvedov about the $L_p$-cohomology of warped cylinders to $L_{p,q}$-cohomology for different $p$ and $q$. As an application, we establish some sufficient conditions for the nontriviality of the $L_{p,q}$-torsion of a surface of revolution in terms of some Hardy constants.