A note on compactness properties of the singular Toda system

Abstract

In this note, we consider blow-up for solutions of the $SU(3)$ Toda system on a compact surface $\Sigma$. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods.