<div class="csl-bib-body">
<div class="csl-entry">Ebenfelt, P., Kossovskij, I., & Lamel, B. (2022). The equivalence theory for infinite type hypersurfaces in ℂ<sup>2</sup>. <i>Transactions of the American Mathematical Society</i>, <i>375</i>(12), 4019–4056. https://doi.org/10.1090/tran/8627</div>
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dc.identifier.issn
0002-9947
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/190400
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dc.description.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.
en
dc.language.iso
en
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dc.publisher
AMER MATHEMATICAL SOC
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dc.relation.ispartof
Transactions of the American Mathematical Society
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dc.subject
CR geometry
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dc.subject
holomorphic mappings
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dc.subject
normal forms
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dc.title
The equivalence theory for infinite type hypersurfaces in ℂ²