The asymptotic behaviour of $p$-capacitary potentials in Asymptotically Conical manifolds

TL;DR

This paper investigates the long-term behavior of $p$-capacitary potentials and inverse mean curvature flow on asymptotically conical manifolds with nonnegative Ricci curvature, revealing their asymptotic properties.

Contribution

It provides new insights into the asymptotic behavior of $p$-capacitary potentials and inverse mean curvature flow on asymptotically conical manifolds with nonnegative Ricci curvature.

Findings

Asymptotic behavior characterized for $p$-capacitary potentials.

Analysis of weak inverse mean curvature flow on these manifolds.

Results applicable to geometric analysis on non-compact manifolds.

Abstract

We study the asymptotic behaviour of the $p$-capacitary potential and of the weak Inverse Mean Curvature Flow of a bounded set along the ends of an Asymptotically Conical Riemannian manifolds with asymptotically nonnegative Ricci curvature.