We studied conformal mappings on Carnot groups of type $(2, 1, \ldots, 1)$ and type $(2, 1, \ldots, 1, 2)$. First, for each class, we constructed an explicit CR submanifold $M_0$ and a diffeomorphism $ T:M_0\to G $ that is a CR diffeomorphism and a Carnot–Carathéodory isometry. Second, for each conformal mapping $f$ on a connected domain in $G$, we prove that the mapping $ T^{-1}\circ f\circ T $ is either CR or anti-CR on $M_0$.
Citation: Junyi Jia, Jie Li. CR and anti-CR rigidity of conformal mappings on two classes of rank-two Carnot groups[J]. AIMS Mathematics, 2026, 11(8): 25170-25191. doi: 10.3934/math.20261012
We studied conformal mappings on Carnot groups of type $(2, 1, \ldots, 1)$ and type $(2, 1, \ldots, 1, 2)$. First, for each class, we constructed an explicit CR submanifold $M_0$ and a diffeomorphism $ T:M_0\to G $ that is a CR diffeomorphism and a Carnot–Carathéodory isometry. Second, for each conformal mapping $f$ on a connected domain in $G$, we prove that the mapping $ T^{-1}\circ f\circ T $ is either CR or anti-CR on $M_0$.
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Junyi Jia, Jie Li. CR and anti-CR rigidity of conformal mappings on two classes of rank-two Carnot groups[J]. AIMS Mathematics, 2026, 11(8): 25170-25191. doi: 10.3934/math.20261012
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