On the $L_{q,p}$-cohomology of Riemannian Manifolds with Negative Curvature

TL;DR

This paper investigates the $L_{q,p}$-cohomology of negatively curved Riemannian manifolds, establishing conditions under which this cohomology does not vanish, thereby advancing understanding of geometric analysis in such spaces.

Contribution

It provides a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected negatively curved manifolds, a novel insight in geometric analysis.

Findings

Non-vanishing of $L_{q,p}$-cohomology under certain curvature conditions

Extension of cohomological techniques to negatively curved manifolds

New criteria for cohomology non-vanishing in geometric contexts

Abstract

We prove a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.