2015/07/22 by Ilya Kossovskiy, Kossovskiy, Ilya, Bernhard Lamel +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV
paper · pdf · doi:10.48550/arxiv.1507.06151
arxiv created 2015/07/22 · openalex publication_date 2015/07/22 · arxiv updated 2015/07/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In our recent work [25] we showed that C^∞ CR-diffeomorphisms of real-analytic Levi-nonflat hypersurfaces in \mathbb C2 are not analytic in general. This result raised again the question on the nature of CR-maps of real-analytic hypersurfaces. In this paper, we give a complete picture of what CR-maps actually are. First, we discover an analytic continuation phenomenon for CR-diffeomorphisms which we call the \em sectorial analyticity property. It appears to be the optimal regularity property for CR-diffeomorphisms in general. We emphasize that such type of extension never appeared previously in the literature. Second, we introduce the class of \em Fuchsian type hypersurfaces and prove that (infinitesimal generators of) CR-automorphisms of a Fuchsian type hypersurface are still analytic. In particular, this solves a problem formulated in [28]. Finally, we prove a regularity result for \em formal CR-automorphisms of Fuchsian type hypersurfaces.