The Catlin Multitype and Biholomorphic Equivalence of Models

Kolář, Martin

doi:10.1093/imrn/rnq013

Cited by 20 publications

(28 citation statements)

References 19 publications

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“…Let us remark that the problem of biholomorphic equivalence of models is considered in [14]. The following result was obtained there.…”

Section: Definition 42 a Transformationmentioning

confidence: 89%

“…Thus we have proved that whenever M is different from S k , all local automorphisms in normal coordinates are of the form (14). Hence it remains to consider the action of (14) on the defining equation of M .…”

Section: Local Automorphism Groups In Cmentioning

confidence: 91%

“…proof: First we will prove that in normal coordinates all local automorphisms of M are decoupled linear, of the form (14). By Proposition 3.1, it remains to consider the case e < k 2 .…”

Section: Local Automorphism Groups In Cmentioning

confidence: 97%

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Higher Order invariants of Levi Degenerate Hypersurfaces

Kolář¹

2010

Pure and Applied Mathematics Quarterly

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The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and analogous results for finite groups. The second part considers hypersurfaces of finite Catlin multitype, and the Kohn-Nirenberg phenomenon in higher dimensions. We give a necessary condition for local convexifiability of a class of pseudoconvex hypersurfaces in C n+1 .

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“…Let us remark that the problem of biholomorphic equivalence of models is considered in [14]. The following result was obtained there.…”

Section: Definition 42 a Transformationmentioning

confidence: 89%

Section: Local Automorphism Groups In Cmentioning

confidence: 91%

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Higher Order invariants of Levi Degenerate Hypersurfaces

Kolář¹

2010

Pure and Applied Mathematics Quarterly

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“…In this section we introduce notation and recall briefly some needed definitions (for more details, see e.g. [20]).…”

Section: Preliminariesmentioning

confidence: 99%

Nonlinear CR automorphisms of Levi degenerate hypersurfaces and a new gap phenomenon

Kolář¹,

Meylan²

2019

Annali Scuola Normale Superiore - Classe Di Scienze

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We give a complete classification of polynomial models for smooth real hypersurfaces of finite Catlin multitype in C 3 , which admit nonlinear infinitesimal CR automorphisms. As a consequence, we obtain a sharp 1-jet determination result for any smooth hypersurface with such model. The results also prove a conjecture of the first author about the origin of such nonlinear automorphisms (AIM list of problems, 2010). As another consequence, we describe all possible dimensions of the Lie algebra of infinitesimal CR automorphisms, which leads to a new "secondary" gap phenomenon.

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“…If M is of finite multitype at p, the infimum in (2.3) is attained, which implies that multitype coordinates do exist ( [9], [25]). Definition 2.4.…”

Section: Preliminariesmentioning

confidence: 99%

Higher order symmetries of real hypersurfaces in ℂ³

Kolář

Meylan-Rivier

2016

Proc. Amer. Math. Soc.

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We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By results of [23], the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear vector fields of arbitrarily high degree, which has no analog in the classical Levi nondegenerate case, or in the case of finite type hypersurfaces in C 2 . We analyze this phenomenon for hypersurfaces of finite Catlin multitype in complex dimension three. The results provide a complete classification of such manifolds. As a consequence, we show on which hypersurfaces 2-jets are not sufficient to determine an automorphism. The results also confirm a conjecture about the origin of nonlinear automorphisms of Levi degenerate hypersurfaces, formulated by the first author (AIM 2010).

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The Catlin Multitype and Biholomorphic Equivalence of Models

Cited by 20 publications

References 19 publications

Higher Order invariants of Levi Degenerate Hypersurfaces

Higher Order invariants of Levi Degenerate Hypersurfaces

Nonlinear CR automorphisms of Levi degenerate hypersurfaces and a new gap phenomenon

Higher order symmetries of real hypersurfaces in ℂ³

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