The equivalence theory for infinite type hypersurfaces in $\mathbb {C}^{2}$
- Author(s)
- Peter Ebenfelt, Ilya Kossovskiy, Bernhard Lamel
- Abstract
We develop a classification theory for real-analytic hypersurfaces in C
2 in the case when the hypersurface is of infinite type at the reference point. This is the remaining, not yet understood case in C
2 in the Problème local, formulated by H. Poincaré in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results is a notion of smooth normal forms for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR-DS technique in CR-geometry.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- University of California, San Diego, Masaryk University
- Journal
- Transactions of the American Mathematical Society
- Volume
- 375
- Pages
- 4019 - 4056
- No. of pages
- 38
- ISSN
- 0002-9947
- DOI
- https://doi.org/10.1090/tran/8627
- Publication date
- 03-2022
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- ASJC Scopus subject areas
- Applied Mathematics, Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/the-equivalence-theory-for-infinite-type-hypersurfaces-in-mathbb-c2(e442e797-3bdc-4be9-b9c9-dd35957b9800).html