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://ucrisportal.univie.ac.at/en/publications/the-equivalence-theory-for-infinite-type-hypersurfaces-in-mathbb-c2(e442e797-3bdc-4be9-b9c9-dd35957b9800).html