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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • 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