Sharp Moser-Trudinger inequalities on Riemannian manifolds with Negative curvature

TL;DR

This paper establishes sharp Moser-Trudinger inequalities on complete, simply connected Riemannian manifolds with negative curvature, extending classical results to curved geometric settings.

Contribution

It provides the first sharp Moser-Trudinger inequalities specifically tailored for negatively curved Riemannian manifolds.

Findings

Derived inequalities with optimal constants for negatively curved manifolds

Extended classical Euclidean inequalities to curved geometric contexts

Enhanced understanding of functional inequalities in geometric analysis

Abstract

Let $M$ be a complete, simply connected Riemannian manifold with negative curvature. We obtain some Moser-Trudinger inequalities with sharp constants on $M$.