Estimates of bubbling solutions of SU(3) Toda systems at critical parameters-Part 2

2022/06/16 by Wei, Juncheng, Wu, Lina, Zhang, Lei
#35B40 #58J05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.08114

Abstract

In this article we study bubbling solutions of regular SU(3) Toda systems defined on a Riemann surface. There are two major difficulties corresponding to the profile of bubbling solutions: partial blowup phenomenon and bubble accumulation. We prove that when both parameters tend to critical positions, if there is one fully bubbling blowup point, then under one curvature assumption, all the blowup solutions near a blowup point satisfy a spherical Harnack inequality, which completely rules out the bubble-accumulation phenomenon. This fact is crucial for a number of applications.

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