New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

TL;DR

This paper introduces enhanced Moser-Trudinger inequalities that are scale-invariant and applies them to establish new existence results for singular Liouville equations on compact surfaces, relevant to Chern-Simons vortices.

Contribution

It develops improved, scale-invariant Moser-Trudinger inequalities and uses them to prove existence results for singular Liouville equations on compact surfaces.

Findings

New existence results for singular Liouville equations.

Development of scale-invariant Moser-Trudinger inequalities.

Application to Chern-Simons vortex models.

Abstract

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.