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PreprintarXiv licencearXiv

Conical Singularities of Toda Solutions with One Finite-Energy Component and Classification on the Punctured Plane

  • Fangyuan Li
  • Jingyu Mu
  • Zhaohu Nie
  • Yiqian Shi
  • Chunhui Wei
  • Bin Xu
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Abstract

We study Toda systems associated with arbitrary complex simple Lie algebras. For solutions on a punctured disc, we prove that finite energy of at least one component near the puncture forces every component to have a conical singularity there. On the punctured plane, we give a geometric formulation and proof of the Lin--Nie--Wei classification of solutions with prescribed cone exponents at the origin and finite total energy in at least one component. We express the parameter space as the complex centralizer of the monodromy modulo a maximal compact subgroup. We also recover the formulas of Karmakar--Lin--Nie--Wei for the cone exponents at infinity and the total energies of the components.

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Cite

BibTeXRIS
BibTeX
@misc{li2026conical,
  title = {{Conical Singularities of Toda Solutions with One Finite-Energy Component and Classification on the Punctured Plane}},
  author = {Fangyuan Li and Jingyu Mu and Zhaohu Nie and Yiqian Shi and Chunhui Wei and Bin Xu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.11919},
  eprint = {2611.11919},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.11919},
}
RIS
TY  - UNPB
TI  - Conical Singularities of Toda Solutions with One Finite-Energy Component and Classification on the Punctured Plane
AU  - Fangyuan Li
AU  - Jingyu Mu
AU  - Zhaohu Nie
AU  - Yiqian Shi
AU  - Chunhui Wei
AU  - Bin Xu
PY  - 2026
DA  - 2026/11/09
PB  - arXiv
DO  - 10.48550/arxiv.2611.11919
UR  - https://arxiv.org/abs/2611.11919
AB  - We study Toda systems associated with arbitrary complex simple Lie algebras. For solutions on a punctured disc, we prove that finite energy of at least one component near the puncture forces every component to have a conical singularity there. On the punctured plane, we give a geometric formulation and proof of the Lin--Nie--Wei classification of solutions with prescribed cone exponents at the origin and finite total energy in at least one component. We express the parameter space as the complex centralizer of the monodromy modulo a maximal compact subgroup. We also recover the formulas of Karmakar--Lin--Nie--Wei for the cone exponents at infinity and the total energies of the components.
ER  -