An algebraic construction of a solution to the mean field equations on hyperelliptic curves and its adiabatic limit
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- by Jia-Ming (Frank) Liou and Chih-Chung Liu PDF
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Abstract:
In this paper, we give an algebraic construction of the solution to the following mean field equation: \begin{equation*} \Delta \psi +e^{\psi }=4\pi \sum _{i=1}^{2g+2}\delta _{P_{i}} \end{equation*} 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 $X.$References
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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
- MR Author ID: 1063388
- Email: cliu@mail.ncku.edu.tw
- Received by editor(s): June 29, 2017
- Published electronically: May 15, 2018
- Communicated by: Lei Ni
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3693-3707
- MSC (2010): Primary 14H55, 35J15
- DOI: https://doi.org/10.1090/proc/14054
- MathSciNet review: 3825825