Huber's theorem for manifolds with $L^\frac{n}{2}$ integrable Ricci curvatures

TL;DR

This paper extends Huber's theorem to higher-dimensional manifolds that are conformally compact with Ricci curvatures in the $L^{n/2}$ space, broadening the understanding of geometric compactification under weaker curvature conditions.

Contribution

It generalizes Huber's finite point conformal compactification theorem to higher dimensions with $L^{n/2}$ Ricci curvature integrability.

Findings

Established a higher-dimensional analogue of Huber's theorem.

Demonstrated conformal compactification under $L^{n/2}$ Ricci curvature conditions.

Extended geometric analysis to manifolds with weaker curvature integrability.

Abstract

In this paper, we generalize Huber's finite point conformal compactification theorem to a higher dimensional manifold, which is conformally compact with $L^\frac{n}{2}$ integrable Ricci curvatures.