### Abstract

We study the Liouville equation Δµ = −e^{2u} in the complex plane with prescribed singularities and obtain a necessary and sufficient condition for the existence of the solution. The proof is based on the continuity method and a uniqueness theorem.

Original language | English (US) |
---|---|

Pages (from-to) | 1119-1129 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 116 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1992 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Liouville equation and spherical convex polytopes'. Together they form a unique fingerprint.

## Cite this

Luo, F., & Tian, G. (1992). Liouville equation and spherical convex polytopes.

*Proceedings of the American Mathematical Society*,*116*(4), 1119-1129. https://doi.org/10.1090/S0002-9939-1992-1137227-5