Classification and nondegeneracy of SU(n+1) Toda system with singular sources
Journal
Inventiones Mathematicae
Journal Volume
190
Journal Issue
1
Pages
169-207
Date Issued
2012
Author(s)
Abstract
We consider the following Toda system, where γ i>-1, δ 0 is Dirac measure at 0, and the coefficients a ij form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: This generalizes the classification result by Jost and Wang for γ i=0, ∀1≤i≤n. (ii) We prove that if γ i+γ i+1+⋯+γ j∉ℤ for all 1≤i≤j≤n, then any solution u i is radially symmetric w. r. t. 0. (iii) We prove that the linearized equation at any solution is non-degenerate. These are fundamental results in order to understand the bubbling behavior of the Toda system. © 2012 Springer-Verlag.
Type
journal article