Optimal Trudinger-Moser inequalities on complete noncompact Riemannian manifolds: Revisit of the argument from the local inequalities to global ones

TL;DR

This paper revisits the proof of a key inequality on Riemannian manifolds, providing a simplified and alternative approach to derive global Trudinger-Moser inequalities from local ones.

Contribution

It offers a simplified and alternative proof method for establishing global Trudinger-Moser inequalities on complete noncompact Riemannian manifolds.

Findings

Simplified proof of Theorem 1.3 from [11]

Alternative argument from local to global inequalities

Enhanced understanding of Trudinger-Moser inequalities on manifolds

Abstract

The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.