J 2016

New extension phenomena for solutions of tangential Cauchy-Riemann equations

KOSSOVSKIY, Ilya a B. LAMEL

Základní údaje

Originální název

New extension phenomena for solutions of tangential Cauchy-Riemann equations

Autoři

KOSSOVSKIY, Ilya (643 Rusko, domácí) a B. LAMEL (620 Portugalsko)

Vydání

Communications in Partial Differential Equations, Philadelphia, PA, USA, Taylor & Francis, 2016, 0360-5302

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 1.608

Kód RIV

RIV/00216224:14310/16:00094221

Organizační jednotka

Přírodovědecká fakulta

DOI

UT WoS

000378746100004

Klíčová slova anglicky

holomorphic maps; CR-functions

Štítky

Změněno: 11. 5. 2017 18:50, Ing. Andrea Mikešková

Anotace

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.