Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.sciencedirect.com/science/article/pii/S0001870821005569 |
| Doi | http://dx.doi.org/10.1016/j.aim.2021.108117 |
| Keywords | CR-manifolds; Holomorphic maps; Analytic continuation; Summability of divergent power series |
| Description | 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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