Ebenfelt, P., Kossovskij, I., & Lamel, B. (2022). The equivalence theory for infinite type hypersurfaces in ℂ2. Transactions of the American Mathematical Society, 375(12), 4019–4056. https://doi.org/10.1090/tran/8627
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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Journal:
Transactions of the American Mathematical Society
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ISSN:
0002-9947
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Date (published):
2022
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Number of Pages:
38
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Publisher:
AMER MATHEMATICAL SOC
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Peer reviewed:
Yes
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Keywords:
CR geometry; holomorphic mappings; normal forms
en
Abstract:
We develop a classification theory for real-analytic hypersurfaces in C² in the case when the hypersurface is of infinite type at the reference point. This is the remaining, not yet understood case in C² 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.
