Effective vanishing order of the Levi determinant

Nicoara, Andreea C.

doi:10.1007/s00208-011-0742-4

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…There are several possible proofs in the literature for the existence of the nonvanishing point of the determinant of the Levi form near a point of finite type. See for example [Nic12] or the forthcoming thesis of Fassina [Fas20]. Nevertheless, we choose the strictly pseudoconvex point z • above only for the simplicity of the construction of our example and it is not required.…”

Section: A Sharp Examplementioning

confidence: 99%

Bekollé-Bonami estimates on some pseudoconvex domains

Huo¹,

Wagner²,

Wick³

2020

Preprint

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We establish a weighted L p norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted L p norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in C 2 , a convex domain of finite type in C n , or a decoupled domain of finite type in C n . The upper bound is related to the Bekollé-Bonami constant and is sharp. When the domain is smooth, bounded, and strictly pseudoconvex, we also obtain a lower bound for the weighted norm.

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Section: A Sharp Examplementioning

confidence: 99%

Bekollé-Bonami estimates on some pseudoconvex domains

Huo¹,

Wagner²,

Wick³

2020

Preprint

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“…See [3] for full details or [6] for a comprehensive outline. We start with Kohn's definition of a subelliptic multiplier.…”

Section: The Kohn Algorithmmentioning

confidence: 99%

Coherence and other properties of sheaves in the Kohn algorithm

Nicoara

2014

Int. J. Math.

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In the smooth case, we prove quasi-flasqueness for the sheaves of all subelliptic multipliers as well as at each of the steps of the Kohn algorithm on a pseudoconvex domain in C n . We use techniques by Jean-Claude Tougeron to show that if the domain has a realanalytic defining function, the modified Kohn algorithm involving generating ideals and taking real radicals only in the ring of real-analytic germs yields quasi-coherent sheaves. This sharpens a result obtained by J. J. Kohn in 1979.

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Proper holomorphic mappings of balanced domains in $$\mathbb {C}^n$$ C n

Janardhanan

2015

Math. Z.

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Abstract. We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in C n , n > 1. Specifically: we prove that any proper holomorphic selfmap of a certain type of balanced, finite-type domain in C n , n > 1, is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

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Effective vanishing order of the Levi determinant

Cited by 6 publications

References 18 publications

Bekollé-Bonami estimates on some pseudoconvex domains

Bekollé-Bonami estimates on some pseudoconvex domains

Coherence and other properties of sheaves in the Kohn algorithm

Proper holomorphic mappings of balanced domains in $$\mathbb {C}^n$$ C n

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