Explicit Solutions to the mean field equations on hyperelliptic curves of genus two

Jia Ming (Frank) Liou

doi:10.1016/j.difgeo.2017.08.005

Explicit Solutions to the mean field equations on hyperelliptic curves of genus two

Jia Ming (Frank) Liou

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let X be a complex hyperelliptic curve of genus two equipped with the canonical metric ds². We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of (X,ds²) determines an explicit solution to a mean field equation.

Original language	English
Pages (from-to)	173-186
Number of pages	14
Journal	Differential Geometry and its Application
Volume	56
DOIs	https://doi.org/10.1016/j.difgeo.2017.08.005
Publication status	Published - 2018 Feb 1

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology
Computational Theory and Mathematics

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title = "Explicit Solutions to the mean field equations on hyperelliptic curves of genus two",

abstract = "Let X be a complex hyperelliptic curve of genus two equipped with the canonical metric ds2. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of (X,ds2) determines an explicit solution to a mean field equation.",

author = "Liou, {Jia Ming (Frank)}",

note = "Funding Information: We are indebted to Prof. C.S. Lin and Prof. C.L. Wang from the National Taiwan university for introducing us the topic of mean field equations. Without them, this paper would not appear. The author was partially supported by MOST 104-2115-M-006-014 Grant, and by the Headquarters of University Advancement at National Cheng Kung University , which is sponsored the Ministry of Education, Republic of China (Taiwan) , and by NCTS . The author also would like to thank the referees for their valuable comments which helped to improve the manuscript. Funding Information: We are indebted to Prof. C.S. Lin and Prof. C.L. Wang from the National Taiwan university for introducing us the topic of mean field equations. Without them, this paper would not appear. The author was partially supported by MOST 104-2115-M-006-014 Grant, and by the Headquarters of University Advancement at National Cheng Kung University, which is sponsored the Ministry of Education, Republic of China (Taiwan), and by NCTS. The author also would like to thank the referees for their valuable comments which helped to improve the manuscript. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = feb,

day = "1",

doi = "10.1016/j.difgeo.2017.08.005",

language = "English",

volume = "56",

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journal = "Differential Geometry and its Applications",

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T1 - Explicit Solutions to the mean field equations on hyperelliptic curves of genus two

AU - Liou, Jia Ming (Frank)

N1 - Funding Information: We are indebted to Prof. C.S. Lin and Prof. C.L. Wang from the National Taiwan university for introducing us the topic of mean field equations. Without them, this paper would not appear. The author was partially supported by MOST 104-2115-M-006-014 Grant, and by the Headquarters of University Advancement at National Cheng Kung University , which is sponsored the Ministry of Education, Republic of China (Taiwan) , and by NCTS . The author also would like to thank the referees for their valuable comments which helped to improve the manuscript. Funding Information: We are indebted to Prof. C.S. Lin and Prof. C.L. Wang from the National Taiwan university for introducing us the topic of mean field equations. Without them, this paper would not appear. The author was partially supported by MOST 104-2115-M-006-014 Grant, and by the Headquarters of University Advancement at National Cheng Kung University, which is sponsored the Ministry of Education, Republic of China (Taiwan), and by NCTS. The author also would like to thank the referees for their valuable comments which helped to improve the manuscript. Publisher Copyright: © 2017 Elsevier B.V.

PY - 2018/2/1

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N2 - Let X be a complex hyperelliptic curve of genus two equipped with the canonical metric ds2. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of (X,ds2) determines an explicit solution to a mean field equation.

AB - Let X be a complex hyperelliptic curve of genus two equipped with the canonical metric ds2. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of (X,ds2) determines an explicit solution to a mean field equation.

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JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

SN - 0926-2245

ER -

Explicit Solutions to the mean field equations on hyperelliptic curves of genus two

Abstract

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