Normal forms and degenerate CR singularities

Burcea, Valentin

doi:10.1080/17476933.2016.1170819

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…For Levi-degenerate hypersurfaces in C N , N ≥ 3 satisfying certain special conditions (in addition to the Hormander-Kohn bracket-generating condition) normal form constructions were carried out by Ebenfelt [16,15] and by Kossovskiy-Zaitsev [33]. For results on normal forms for real submanifolds of higher codimension as well as CR-singular submanifolds we refer to Ezhov-Schmalz [18], Beloshapka [4], Lamel-Stolovitch [36], Moser-Webster [39], Huang-Yin [20,21], Gong [19], Coffman [13], Burcea [8]. See also Zaitsev [48] for normal forms in the non-integrable setting.…”

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

Ebenfelt¹,

Kossovskiy²,

Lamel³

2018

Preprint

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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.

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mentioning

confidence: 99%

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

Ebenfelt¹,

Kossovskiy²,

Lamel³

2018

Preprint

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Real submanifolds in complex spaces

Burcea

2016

Acta. Math. Sin.-English Ser.

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Abstract. Let (z 11 , . . . , z 1N , . . . , z m1 , . . . , z mN , w 11 , . . . , wmm ) be the coordinates in C mN +m 2. In this note we prove the analogue of the Theorem of Moser [24] in the case of the real-analytic submanifold M defined as followswhere W = w ij 1≤i,j≤m and Z = z ij 1≤i≤m, 1≤j≤N . We prove that M is biholomorphically equivalent to the model W = ZZ t if and only if is formally equivalent to it.

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The equivalence theory for infinite type hypersurfaces in ℂ²

Ebenfelt

Kossovskiy

Lamel

2022

Trans. Amer. Math. Soc.

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We develop a classification theory for real-analytic hypersurfaces in C 2 \mathbb {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 \mathbb {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.

show abstract

Normal forms and degenerate CR singularities

Cited by 3 publications

References 23 publications

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

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

Real submanifolds in complex spaces

The equivalence theory for infinite type hypersurfaces in ℂ²

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