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

• Autoři: KOSSOVSKIY Ilya; LAMEL B.; STOLOVITCH L.
• Rok publikování: 2022
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Advances in Mathematics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://www.sciencedirect.com/science/article/pii/S0001870821005569
• Doi: http://dx.doi.org/10.1016/j.aim.2021.108117
• Klíčová slova: CR-manifolds; Holomorphic maps; Analytic continuation; Summability of divergent power series
• Popis: We apply the multisummability theory from Dynamical Sys- tems 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 Con- jecture due to N. Mir [29].

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• Klasifikační problémy pro reálné nadplochy v komplexním prostoru