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【学术报告及分析与偏微分方程讨论班(2022春第9讲)】Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric
发布日期:2022-05-06  浏览量:

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--- 分析与偏微分方程讨论班(2022春季第9)


题目: Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric


报告人: 金钢 教授 (北京师范大学)


时间:2022-5-16 1030-1130 (周一上午)


地点: 腾讯会议 ID397-754-224

腾讯会议链接:https://meeting.tencent.com/dm/VCXNO1GT5sE0


摘要: We prove that any positive solution of the Yamabe equation on an asymptotically flat n-dimensional manifold of flatness order at least (n-2)/2 and n ≤ 24 must converge at infinity either to a fundamental solution of the Laplace operator on the Euclidean space or to a radial Fowler solution defined on the entire Euclidean space. The flatness order (n-2)/2 is the minimal flatness order required to define ADM mass in general relativity; the dimension 24 is the dividing dimension of the validity of compactness of solutions to the Yamabe problem. We also prove such alternatives for bounded solutions when n > 24. This is joint with Zheng-Chao Han and Lei Zhang.


报告人简介: 熊金钢,北京师范大学教授,博导。研究方向为偏微分方程、非线性分析和几何分析。在JEMS, AJM, Crelle, Math. Ann. 等国际知名期刊发表论文30余篇,2019年获国家优秀青年基金资助。

 

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