New extension phenomena for solutions of tangential Cauchy-Riemann equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00094221" target="_blank" >RIV/00216224:14310/16:00094221 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/03605302.2016.1180536" target="_blank" >http://dx.doi.org/10.1080/03605302.2016.1180536</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03605302.2016.1180536" target="_blank" >10.1080/03605302.2016.1180536</a>
Alternative languages
Result language
angličtina
Original language name
New extension phenomena for solutions of tangential Cauchy-Riemann equations
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Partial Differential Equations
ISSN
0360-5302
e-ISSN
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Volume of the periodical
41
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
925-951
UT code for WoS article
000378746100004
EID of the result in the Scopus database
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