Isolated singularities for the n-Liouville equation

TL;DR

This paper studies isolated singularities in solutions to the n-Liouville equation, showing they are logarithmic and simplifying classification, leading to a quantization result for entire solutions.

Contribution

It introduces a simplified classification approach for solutions with isolated singularities and establishes a quantization result for entire solutions of the singular n-Liouville equation.

Findings

Solutions with isolated singularities are of logarithmic type.

The classification argument is simplified.

A quantization result for entire solutions is established.

Abstract

In dimension n isolated singularities -- at a finite point or at infinity -- for solutions of finite total mass to the n-Liouville equation are of logarithmic type. As a consequence, we simplify the classification argument in arXiv:1609.03608 and establish a quantization result for entire solutions of the singular n-Liouville equation.