Hardy type inequalities on closed manifolds via Ricci curvature

TL;DR

This paper establishes sharp Hardy type inequalities on closed weighted Riemannian manifolds using weighted Ricci curvatures, extending recent results from noncompact to compact settings.

Contribution

It introduces new Hardy inequalities on closed manifolds leveraging weighted Ricci curvature, filling a gap in the existing literature.

Findings

Sharp Hardy inequalities on closed manifolds

Use of weighted Ricci curvature in inequalities

Extension of noncompact results to compact manifolds

Abstract

The paper is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in several aspects those obtained recently in the noncompact Riemannian setting.