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@article{1376683,
author = {Kossovskiy, Ilya and Lamel, B. and Lamel, Bernhard},
article_location = {Philadelphia, PA, USA},
article_number = {6},
doi = {http://dx.doi.org/10.1080/03605302.2016.1180536},
keywords = {holomorphic maps; CR-functions},
language = {eng},
issn = {0360-5302},
journal = {Communications in Partial Differential Equations},
title = {New extension phenomena for solutions of tangential Cauchy-Riemann equations},
volume = {41},
year = {2016}
}
TY - JOUR
ID - 1376683
AU - Kossovskiy, Ilya - Lamel, B. - Lamel, Bernhard
PY - 2016
TI - New extension phenomena for solutions of tangential Cauchy-Riemann equations
JF - Communications in Partial Differential Equations
VL - 41
IS - 6
SP - 925-951
EP - 925-951
PB - Taylor & Francis
SN - 03605302
KW - holomorphic maps
KW - CR-functions
N2 - 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.
ER -
KOSSOVSKIY, Ilya a B. LAMEL. New extension phenomena for solutions of tangential Cauchy-Riemann equations. \textit{Communications in Partial Differential Equations}. Philadelphia, PA, USA: Taylor \&{} Francis, roč.~41, č.~6, s.~925-951. ISSN~0360-5302. doi:10.1080/03605302.2016.1180536. 2016.
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