Energy concentration and a priori estimates for $B_2$ and $G_2$ types of Toda systems

Abstract

For Toda systems with Cartan matrix either $B_2$ or $G_2$, we prove that the local mass of blowup solutions at its blowup points converges to a finite set. Further more this finite set can be completely determined for $B_2$ Toda systems, while for $G_2$ systems we need one additional assumption. As an application of the local mass classification we establish a priori estimates for corresponding Toda systems defined on Riemann surfaces.

26 pages

References in corpus (1)

• Degree counting and shadow system for $SU(3)$ Toda system: one bubbling

Cited by in corpus (2)

• Degree counting for Toda system with simple singularity : one point blow up
• Sharp estimates for solutions of mean field equation with collapsing singularity