| KOSSOVSKIY, Ilya, B. LAMEL and L. STOLOVITCH. Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory. Advances in Mathematics. Elsevier, 2022, vol. 397, March, p. 1-42. ISSN 0001-8708. Available from: https://dx.doi.org/10.1016/j.aim.2021.108117. |
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@article{1830689,
author = {Kossovskiy, Ilya and Lamel, B. and Stolovitch, L.},
article_number = {March},
doi = {http://dx.doi.org/10.1016/j.aim.2021.108117},
keywords = {CR-manifolds; Holomorphic maps; Analytic continuation; Summability of divergent power series},
language = {eng},
issn = {0001-8708},
journal = {Advances in Mathematics},
title = {Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory},
url = {https://www.sciencedirect.com/science/article/pii/S0001870821005569},
volume = {397},
year = {2022}
}
TY - JOUR
ID - 1830689
AU - Kossovskiy, Ilya - Lamel, B. - Stolovitch, L.
PY - 2022
TI - Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory
JF - Advances in Mathematics
VL - 397
IS - March
SP - 1-42
EP - 1-42
PB - Elsevier
SN - 00018708
KW - CR-manifolds
KW - Holomorphic maps
KW - Analytic continuation
KW - Summability of divergent power series
UR - https://www.sciencedirect.com/science/article/pii/S0001870821005569
N2 - 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].
ER -
KOSSOVSKIY, Ilya, B. LAMEL and L. STOLOVITCH. Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory. \textit{Advances in Mathematics}. Elsevier, 2022, vol.~397, March, p.~1-42. ISSN~0001-8708. Available from: https://dx.doi.org/10.1016/j.aim.2021.108117.
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