Estimates of bubbling sequences of SU(3)$SU(3)$ Toda systems at critical parameters: Part 2

Abstract

AbstractIn this article, we study bubbling sequences of regular Toda systems defined on a Riemann surface. There are two major difficulties corresponding to the profile of bubbling sequences: partial blow up phenomenon and bubble accumulation. We prove that when both parameters tend to critical positions, if there is one fully bubbling blow up point, then under a suitable curvature assumption, all the blow up solutions near the blow up point satisfy a spherical Harnack inequality, which completely rules out the bubble‐accumulation phenomenon. This fact is crucial for a number of applications.