{"paper":{"title":"Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Chang-shou Lin, Dong Ye, Juncheng Wei","submitted_at":"2011-11-02T05:36:02Z","abstract_excerpt":"We consider the following Toda system\n\\Delta u_i + \\D \\sum_{j = 1}^n a_{ij}e^{u_j} = 4\\pi\\gamma_{i}\\delta_{0}  \\text{in}\\mathbb R^2,   \\int_{\\mathbb R^2}e^{u_i} dx < \\infty,   \\forall 1\\leq i \\leq n,\nwhere $\\gamma_{i} > -1$, $\\delta_0$ 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:\n$$\\sum_{j=1}^n a_{ij}\\int_{\\R^2}e^{u_j} dx = 4\\pi (2+\\gamma_i+\\gamma_{n+1-i}), \\;\\;\\forall\\; 1\\leq i \\leq n.$$\nThis generalizes the classification result by Jost and Wang fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0390","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}