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--- 分析与偏微分方程讨论班(2022春季第9讲)

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

报告人: 熊金钢 教授 （北京师范大学）

时间：2022-5-16 10：30-11：30 (周一上午)

地点: 腾讯会议 ID：397-754-224

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。

邀请人：戴蔚

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