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

Research output: Contribution to journalArticle

### 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 $X.$
Original language English 3693 3707 Proceedings of the American Mathematical Society 146 Published - 2018 Jul

### Fingerprint

Weierstrass Point
Mean Field Equation
Hyperelliptic Curves
Pi
Genus
Metric

### Cite this

@article{acb4c387906a41f49d6f559a41a52ba7,
title = "An algebraic construction of solutions to the mean field equations on hyperelliptic curves and its adiabatic limit",
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 $X.$",
author = "Jia-Ming Liou and Chih-Chung Liu",
year = "2018",
month = "7",
language = "English",
volume = "146",
pages = "3693",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",

}

In: Proceedings of the American Mathematical Society, Vol. 146, 07.2018, p. 3693.

Research output: Contribution to journalArticle

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 -