JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP

doi:10.1007/s10473-025-0121-y

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 264-279.doi: 10.1007/s10473-025-0121-y

JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP

Xinan Ma¹, Qianzhong Ou², Tian Wu¹

1. School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China;
2. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China

收稿日期:2024-10-27 发布日期:2025-02-06
作者简介:Xinan Ma, E-mail,: xinan@ustc.edu.cn; Qianzhong Ou, E-mail,: ouqzh@gxnu.edu.cn; Tian Wu, E-mail,: wt1997@ustc.edu.cn
基金资助:
National Natural Science Foundation of China (12141105, 12471194) and the first author's research also was supported by the National Key Research and Development Project (SQ2020YFA070080).

JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP

Xinan Ma¹, Qianzhong Ou², Tian Wu¹

1. School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China;
2. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China

Received:2024-10-27 Published:2025-02-06
About author:Xinan Ma, E-mail,: xinan@ustc.edu.cn; Qianzhong Ou, E-mail,: ouqzh@gxnu.edu.cn; Tian Wu, E-mail,: wt1997@ustc.edu.cn
Supported by:
National Natural Science Foundation of China (12141105, 12471194) and the first author's research also was supported by the National Key Research and Development Project (SQ2020YFA070080).

摘要/Abstract

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 [5]. 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.

关键词: Cauchy-Riemann Yamabe problem, subelliptic equations, Jerison-Lee identities

Abstract: 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 [5]. 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.

Key words: Cauchy-Riemann Yamabe problem, subelliptic equations, Jerison-Lee identities

中图分类号:

32V20

Xinan Ma, Qianzhong Ou, Tian Wu. JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP[J]. 数学物理学报(英文版), 2025, 45(1): 264-279.

Xinan Ma, Qianzhong Ou, Tian Wu. JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP[J]. Acta mathematica scientia,Series B, 2025, 45(1): 264-279.

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JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP

JERISON-LEE IDENTITIES AND SEMI-LINEAR SUBELLIPTIC EQUATIONS ON HEISENBERG GROUP

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