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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