## Abstract

In this paper, we give an algebraic construction of the solution to the following mean field equation

$$

\Delta \psi+e^{\psi}=4\pi\sum_{i=1}^{2g+2}\delta_{P_{i}},

$$

on a genus $g\geq 2$ hyperelliptic curve $(X,ds^{2})$ where $ds^{2}$ is a canonical metric on $X$ and $\{P_{1},\cdots,P_{2g+2}\}$ is the set of Weierstrass points on $X.$

$$

\Delta \psi+e^{\psi}=4\pi\sum_{i=1}^{2g+2}\delta_{P_{i}},

$$

on a genus $g\geq 2$ hyperelliptic curve $(X,ds^{2})$ where $ds^{2}$ is a canonical metric on $X$ and $\{P_{1},\cdots,P_{2g+2}\}$ is the set of Weierstrass points on $X.$

Original language | English |
---|---|

Pages (from-to) | 3693 |

Number of pages | 3707 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Publication status | Published - 2018 Jul |