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On the curvature equation with four singular sources on flat tori
发布时间: 2017-12-08     18:41   【返回上一页】 发布人:陈志杰


 

北京师范大学数学科学学院

 

周五公众报告

 

 

报告题目:On the curvature equation with four singular sources on flat tori

报告人:陈志杰(清华大学)

时间地点:1215日,1600—1700 后主楼1124

邀请人:熊金钢

报告摘要:I will introduce some recent advances on the curvature equation with four singular sources $/Delta u+e^{u}=8/pi /sum_{k=0}^3 n_k /delta_{/omega_k/2}$ on $E_{/tau}$ , $n_k N$, where $E_{/tau}$ is a flat torus and $/delta_{/omega_k/2}$ is the Dirac measure at the half period $/omega_k/2$’s. The solvability of this equation depends essentially on the geometry of $E_{/tau}$ and is challenging from the PDE point of view. I will mainly introduce a sharp nonexistence result for rectangular tori. We also introduce how to apply the nonexistence for rectangular tori to obtain the existence for rhombus tori. This is mainly based on a joint work with Professor ChangShou Lin.

 

 

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