Jerison-Lee identity and Semi-linear subelliptic equation on CR manifold

：麻希南（中国科学技术大学）
：2025-05-24 15:00
：海韵园实验楼S102报告厅

报告人：麻希南（中国科学技术大学）

时  间：2025年5月24日15:00

地  点：海韵园实验楼S102报告厅

内容摘要:

In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR) Yamabe problem, Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg group $\mathbb H^n$ by using the computer in \cite{MR0924699}. They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae. With the help of dimension conservation and invariant tensors, we can answer the above question. For a class of subcritical exponent subelliptic equations on the CR manifold, several new types of differential identities are found. Then we use those identities to get the rigidity result, where rigidity means that subelliptic equations have no other solution than some constant at least when parameters are in a certain range. The rigidity result also deduces the sharp Folland-Stein inequality on closed CR manifolds.  At last we shall mention some related problems on this technique, for example p-Laplace equation, Engel group, Heisenberg type group. This is the joint work with Qanzhong OU, Tian WU.

个人简介：

麻希南，中国科学技术大学数学系教授、中法英才班中方负责人，主要从事椭圆偏微分方程与几何分析的理论研究，在Monge-Ampere方程、经典凸几何与微分方程的几何性态等方面研取得一系列重要研究成果。曾先后受邀访问美国普林斯顿高等研究院、法国高等研究院(IHES)、美国明尼苏达大学、加拿大麦吉尔大学等国际知名高校和研究机构，已在Invent. Math.，CPAM，Memoirs of AMS，J. Reine Angew. Math.，CMP，Adv. Math.等国际一流期刊发表高水平学术论文50多篇。曾先后获霍英东基金会研究奖，入选教育部新世纪优秀人才支持计划、中科院百人计划，2011年获国家杰出青年基金，2013年入选国家级重大人才计划。

 

 

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