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.
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
.
DOI: 10.1007/s10473-025-0121-y
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