The p-Hyperbolicity of Infinity Volume Ends and Applications

TL;DR

This paper characterizes p-hyperbolic ends on complete Riemannian manifolds that satisfy a Sobolev inequality, providing insights into their geometric and analytical properties.

Contribution

It offers a new characterization of p-hyperbolic ends based on Sobolev inequalities on complete Riemannian manifolds.

Findings

Characterization of p-hyperbolic ends using Sobolev inequalities

Conditions under which ends are p-hyperbolic

Applications to geometric analysis of manifolds

Abstract

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.