Detailed Information on Publication Record
2016
New extension phenomena for solutions of tangential Cauchy-Riemann equations
KOSSOVSKIY, Ilya and B. LAMELBasic 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
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
Impact factor
Impact factor: 1.608
RIV identification code
RIV/00216224:14310/16:00094221
Organization unit
Faculty of Science
UT WoS
000378746100004
Keywords in English
holomorphic maps; CR-functions
Změněno: 11/5/2017 18:50, Ing. Andrea Mikešková
Abstract
V originále
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.