KOSSOVSKIY, Ilya and B. LAMEL. New extension phenomena for solutions of tangential Cauchy-Riemann equations. Communications in Partial Differential Equations. Philadelphia, PA, USA: Taylor & Francis, vol. 41, No 6, p. 925-951. ISSN 0360-5302. doi:10.1080/03605302.2016.1180536. 2016.
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Basic information
Original name New extension phenomena for solutions of tangential Cauchy-Riemann equations
Authors KOSSOVSKIY, Ilya (643 Russian Federation, belonging to the institution) and B. LAMEL (620 Portugal).
Edition Communications in Partial Differential Equations, Philadelphia, PA, USA, Taylor & Francis, 2016, 0360-5302.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 1.608
RIV identification code RIV/00216224:14310/16:00094221
Organization unit Faculty of Science
Doi http://dx.doi.org/10.1080/03605302.2016.1180536
UT WoS 000378746100004
Keywords in English holomorphic maps; CR-functions
Tags AKR, rivok
Changed by Changed by: Ing. Andrea Mikešková, učo 137293. Changed: 11/5/2017 18:50.
Abstract
In our recent work, we showed that smooth CR-diffeomorphisms of real-analytic Levi-nonflat hypersurfaces in C^2 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-dieomorphisms which we call the sectorial analyticity property. It appears to be the optimal regularity property for CR-dieomorphisms in general. We emphasize that such type of extension never appeared previously in the literature. Second, we introduce the class of Fuchsian type hypersurfaces and prove that (innitesimal generators of) CR-automorphisms of a Fuchsian type hypersurface are still analytic. In particular, this solves a problem formulated earlier by Shafikov and the first author. Finally, we prove a regularity result for formal CR-automorphisms of Fuchsian type hypersursufaces.
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