A Theory Connecting Mean Field Equations on Tori and Painlev(e) Ⅵ Equation

来源 :非线性偏微分方程和数学物理研讨会(NPDEMP 2016) | 被引量 : 0次 | 上传用户：liongliong530

【摘要】

：

　　We develop a new theory to connect two areas:(ⅰ)Painlev(e)Ⅵ equation and(ⅱ)the mean field equation with multiple singular sources on tori.This gives a ge

【作者】

：

Zhijie Chen

【机构】

：

TsinghuaUniversity

【出处】

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非线性偏微分方程和数学物理研讨会(NPDEMP 2016)

【发表日期】

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2016年12期

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　　We develop a new theory to connect two areas:(ⅰ)Painlev(e)Ⅵ equation and(ⅱ)the mean field equation with multiple singular sources on tori.This gives a geometric interpretation of solutions to Painlev(e)Ⅵ equation with some special parameters.We establish this theory by applying a generalized Lam(e) equation(a linear ODE).As an application,we obtain a sharp existence result for the mean field equation on tori.This is a joint work with Professors Chang-Shou Lin and Ting-Jung Kuo.

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A Theory Connecting Mean Field Equations on Tori and Painlev(e) Ⅵ Equation

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