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


Authors: Jia-Ming (Frank) Liou and Chih-Chung Liu
Journal: Proc. Amer. Math. Soc. 146 (2018), 3693-3707
MSC (2010): Primary 14H55, 35J15
DOI: https://doi.org/10.1090/proc/14054
Published electronically: May 15, 2018
MathSciNet review: 3825825
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Abstract: In this paper, we give an algebraic construction of the solution to the following mean field equation:

$\displaystyle \Delta \psi +e^{\psi }=4\pi \sum _{i=1}^{2g+2}\delta _{P_{i}}$    

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.$

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Additional Information

Jia-Ming (Frank) Liou
Affiliation: Department of Mathematics, National Cheng Kung University, Taiwan — and — NCTS, Mathematics
Email: fjmliou@mail.ncku.edu.tw

Chih-Chung Liu
Affiliation: Department of Mathematics, National Cheng Kung University, Taiwan
Email: cliu@mail.ncku.edu.tw

DOI: https://doi.org/10.1090/proc/14054
Received by editor(s): June 29, 2017
Published electronically: May 15, 2018
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society