Sharp Sobolev and Moser-Trudinger inequalities on noncompact Riemannian manifolds with Ricci curvature bounded below

TL;DR

This paper proves optimal Sobolev and Moser-Trudinger inequalities on certain noncompact Riemannian manifolds with Ricci curvature bounds, advancing understanding of geometric analysis in these settings.

Contribution

It establishes sharp inequalities with best constants on noncompact manifolds under Ricci curvature and injectivity radius conditions, extending classical results.

Findings

Optimal Sobolev inequalities with best constants

Sharp Moser-Trudinger inequalities on noncompact manifolds

Results applicable to manifolds with Ricci curvature bounded below

Abstract

We establish Sobolev and Moser-Trudinger inequalities with best constants on noncompact Riemannan manifolds with Ricci curvature bounded below, and positive injectivity radius.