TY - JOUR
T1 - Classification and nondegeneracy of SU(n+1) Toda system with singular sources
AU - Lin, Chang Shou
AU - Wei, Juncheng
AU - Ye, Dong
PY - 2012/10
Y1 - 2012/10
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84866465270
U2 - 10.1007/s00222-012-0378-3
DO - 10.1007/s00222-012-0378-3
M3 - 文章
AN - SCOPUS:84866465270
SN - 0020-9910
VL - 190
SP - 169
EP - 207
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -