Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory
- Author(s)
- Bernhard Lamel, Ilya Kossovskiy, Laurent Stolovitch
- 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].
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- Masaryk University, Université Nice-Sophia-Antipolis, Université Côte d'Azur
- Journal
- Advances in Mathematics
- Volume
- 397
- ISSN
- 0001-8708
- DOI
- https://doi.org/10.1016/j.aim.2021.108117
- Publication date
- 03-2022
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- Keywords
- ASJC Scopus subject areas
- Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/equivalence-of-threedimensional-cauchyriemann-manifolds-and-multisummability-theory(1361c1a0-9877-4647-94e9-890664294c57).html