Onofri-type inequalities for singular Liouville equations

TL;DR

This paper investigates the blow-up behavior of sequences minimizing a singular Moser-Trudinger functional on compact surfaces, providing estimates and sharp inequalities related to singularities on the sphere.

Contribution

It introduces new estimates for the infimum of the functional and derives sharp Onofri-type inequalities with singularities on the sphere.

Findings

Estimates for the infimum value of the functional in the absence of minima.

Sharp Onofri-type inequalities for the sphere with up to two singularities.

Analysis of blow-up behavior for minimizing sequences.

Abstract

We study the blow-up behaviour of minimizing sequences for the singular Moser-Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.