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PreprintarXiv licencearXiv

A Parametrization of Solutions to the Liouville Equation in a Punctured Disc

  • Qing Han
  • Jui-Yun Hung
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Abstract

In this paper, we study parametrization of solutions to the Liouville equation near their isolated singular points. We demonstrate that prescribing asymptotic behaviors forms a new type of problem leading to all such solutions. The harmonic functions determining the asymptotic behaviors play the role of ``free data" as the boundary values in the boundary value problems.

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Cite

BibTeXRIS
BibTeX
@misc{han2026parametrization,
  title = {{A Parametrization of Solutions to the Liouville Equation in a Punctured Disc}},
  author = {Qing Han and Jui-Yun Hung},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13702},
  eprint = {2609.13702},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13702},
}
RIS
TY  - UNPB
TI  - A Parametrization of Solutions to the Liouville Equation in a Punctured Disc
AU  - Qing Han
AU  - Jui-Yun Hung
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13702
UR  - https://arxiv.org/abs/2609.13702
AB  - In this paper, we study parametrization of solutions to the Liouville equation near their isolated singular points. We demonstrate that prescribing asymptotic behaviors forms a new type of problem leading to all such solutions. The harmonic functions determining the asymptotic behaviors play the role of ``free data" as the boundary values in the boundary value problems.
ER  -