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arXiv · 1811.01649

The equivalence theory for infinite type hypersurfaces in $\mathbb C^2$

Peter Ebenfelt·Ilya Kossovskiy·Bernhard Lamel
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Abstract

We develop a classification theory for real-analytic hypersurfaces in $\mathbb C^2$ in the case when the hypersurface is of {\em infinite type} at the reference point. This is the remaining, not yet understood case in $\mathbb C^2$ in the {\it Probl\`eme local}, formulated by H.\,Poincar\'e in 1907 and asking for a complete biholomorphic classification of real hypersurfaces in complex space. One novel aspect of our results, appearing in this revised version, is a notion of {\em smooth normal forms} for real-analytic hypersurfaces. We rely fundamentally on the recently developed CR -- DS technique in CR-geometry.

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Peter Ebenfelt, Ilya Kossovskiy, Bernhard Lamel. 2018-11-05. The equivalence theory for infinite type hypersurfaces in $\mathbb C^2$. https://arxiv.org/abs/1811.01649

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