# An algebraic construction of solutions to the mean field equations on hyperelliptic curves and its adiabatic limit

## 摘要

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 $X.$
原文 English 3693 3707 Proceedings of the American Mathematical Society 146 Published - 2018 七月