Cohomologie $L^p$ et pincement

TL;DR

This paper establishes a sharp vanishing theorem for the $L^p$ cohomology torsion of negatively curved Riemannian manifolds with pinched curvature, impacting the understanding of quasiisometric classifications.

Contribution

It introduces a precise vanishing result for $L^p$ cohomology torsion in negatively curved manifolds with pinched curvature, linking geometric curvature conditions to topological invariants.

Findings

Vanishing theorem for $L^p$ cohomology torsion in pinched negative curvature.

Certain negatively curved homogeneous spaces cannot be quasiisometric to better pinched manifolds.

Implications for geometric rigidity and classification of negatively curved spaces.

Abstract

A sharp vanishing theorem for the $L^p$ cohomology torsion of Riemannian manifolds with pinched negative curvature is given. It follows that certain negatively curved homogeneous spaces cannot be quasiisometric to better pinched manifolds.