### Abstract

$$

\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 |

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**An algebraic construction of solutions to the mean field equations on hyperelliptic curves and its adiabatic limit.** / Liou, Jia-Ming; Liu, Chih-Chung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An algebraic construction of solutions to the mean field equations on hyperelliptic curves and its adiabatic limit

AU - Liou, Jia-Ming

AU - Liu, Chih-Chung

PY - 2018/7

Y1 - 2018/7

N2 - 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 $X.$

AB - 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 $X.$

M3 - Article

VL - 146

SP - 3693

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -