On the analyticity of CR-diffeomorphisms
Ilya Kossovskiy, Bernhard Lamel
TL;DR
This paper constructs examples of CR-submanifolds that are smoothly CR-equivalent but not holomorphically equivalent, providing a negative answer to a conjecture about the analyticity of CR-diffeomorphisms.
Contribution
It introduces a method to construct real-analytic, holomorphically nondegenerate CR-submanifolds that are smoothly but not holomorphically equivalent, addressing a longstanding conjecture.
Findings
Existence of CR-submanifolds that are smoothly CR-equivalent but holomorphically inequivalent
Negative resolution of Ebenfelt and Huang's conjecture on CR-diffeomorphism analyticity
Counterexamples in positive CR-dimension and CR-codimension settings
Abstract
In any positive CR-dimension and CR-codimension we provide a construction of real-analytic holomorphically nondegenerate CR-submanifolds, which are CR-equivalent, but are inequivalent holomorphically. As a corollary, we provide the negative answer to the conjecture of Ebenfelt and Huang \cite{eh} on the analyticity of CR-equivalences between real-analytic Levi nonflat hypersurfaces in dimension 2.
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