Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory

Bernhard Lamel; Ilya Kossovskiy; Laurent Stolovitch

doi:10.1016/j.aim.2021.108117

Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory

Bernhard Lamel, Ilya Kossovskiy, Laurent Stolovitch

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in C ² are formally equivalent, if and only if they are C ^∞ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in C ² are algebraic (and in particular convergent). By doing so, we solve a Conjecture due to N. Mir [29].

Original language	English
Article number	108117
Journal	Advances in Mathematics
Volume	397
DOIs	https://doi.org/10.1016/j.aim.2021.108117
Publication status	Published - Mar 2022

Austrian Fields of Science 2012

101002 Analysis

Keywords

Analytic continuation
CR-manifolds
Holomorphic maps
Summability of divergent power series

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10.1016/j.aim.2021.108117

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abstract = "We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in C 2 are formally equivalent, if and only if they are C ∞ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in C 2 are algebraic (and in particular convergent). By doing so, we solve a Conjecture due to N. Mir [29]. ",

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AU - Kossovskiy, Ilya

AU - Stolovitch, Laurent

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N2 - We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in C 2 are formally equivalent, if and only if they are C ∞ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in C 2 are algebraic (and in particular convergent). By doing so, we solve a Conjecture due to N. Mir [29].

AB - We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in C 2 are formally equivalent, if and only if they are C ∞ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in C 2 are algebraic (and in particular convergent). By doing so, we solve a Conjecture due to N. Mir [29].

KW - Analytic continuation

KW - CR-manifolds

KW - Holomorphic maps

KW - Summability of divergent power series

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JO - Advances in Mathematics

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M1 - 108117

ER -

Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory

Abstract

Austrian Fields of Science 2012

Keywords

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