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

In this article, we study bubbling sequences of regular SU(3) 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.