Trudinger-Moser embedding on the hyperbolic space

TL;DR

This paper improves Trudinger-Moser inequalities specifically for hyperbolic space, building on previous work for more general Riemannian manifolds with bounded Ricci curvature and positive injectivity radius.

Contribution

It refines existing inequalities by focusing on hyperbolic space, using a gluing local estimates method to achieve sharper results.

Findings

Enhanced Trudinger-Moser inequalities for hyperbolic space

Method based on gluing local estimates

Improved bounds compared to previous inequalities

Abstract

In [16], we established Trudinger-Moser inequalities for complete noncompact Riemannian manifold on which the Ricci curvature has lower bound and the injectivity radius is strictly positive. In this note, we improve those inequalties when the manifold is the hyperbolic space. The method we used here is still gluing local estimates.