The comparability of the Kobayashi approach region and the admissible approach region

Aladro, Gerardo

doi:10.1215/ijm/1255988804

Cited by 11 publications

(4 citation statements)

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“…We call U α an admissible approach region of the Bergman kernel of Ω f at z 0 . The region U α seems deeply connected with the admissible approach regions studied in [35],[36], [1],[37], etc. We remark that on the region U α , the exchange of the expansion variable ̺ 1 m for r 1 m , where r is a defining function of Ω f (e.g.…”

Section: Statement Of Main Resultsmentioning

confidence: 91%

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\bf C}^2$

Kamimoto¹

1998

Annales De La Faculté Des Sciences De Toulouse Mathématiques

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In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C 2 . Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points is essentially expressed by using two variables ; moreover certain real blowing-up is necessary to understand its singularity. The form of the asymptotic expansion with respect to each variable is similar to that in the strictly pseudoconvex case due to C. Fefferman. We also give an analogous result in the case of the Szegö kernel.

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Section: Statement Of Main Resultsmentioning

confidence: 91%

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\bf C}^2$

Kamimoto¹

1998

Annales De La Faculté Des Sciences De Toulouse Mathématiques

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“…In view of this remark and the inequalities c D ≤ k D ≤ l D , we have the following quantitative information about the Carathéodory/Kobayashi/ Lempert balls of (C-)convex domains. 2 Theorem 1. Let D be a domain in C n , containing no complex lines, and q ∈ D. Assume that the standard basis of C n is minimal for D at q.…”

Section: Introduction and Resultsmentioning

confidence: 99%

The Kobayashi balls of ( $${\mathbb {C}}$$ C -)convex domains

Nikolov

Trybuła

2015

Monatsh Math

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“…respectively where the positive constants C(R) and c(R) are independent of p. It is possible to obtain analogues of this result for weakly pseudoconvex and convex finite type domains without integrating the infinitesimal metric. Such estimates were obtained by Aladro in [1] for weakly pseudoconvex finite type domains in C 2 using a suitable metric on the horizontal subbundle on ∂D due to Nagel-Stein-Wainger [29].…”

Section: Introductionmentioning

confidence: 89%

Some aspects of the Kobayashi and Carathéodory metrics on pseudoconvex domains

Mittal,

Verma

2009

Preprint

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The purpose of this article is to consider two themes both of which emanate from and involve the Kobayashi and the Carathéodory metric. First we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains, on weakly pseudoconvex domains of finite type in C 2 and on convex finite type domains in C n using the scaling method. Applications include an alternate proof of the Wong-Rosay theorem, a characterization of analytic polyhedra with noncompact automorphism group when the orbit accumulates at a singular boundary point and a description of the Kobayashi balls on weakly pseudoconvex domains of finite type in C 2 and convex finite type domains in C n in terms of Euclidean parameters. Second a version of Vitushkin's theorem about the uniform extendability of a compact subgroup of automorphisms of a real analytic strongly pseudoconvex domain is proved for C 1isometries of the Kobayashi and Carathéodory metrics on a smoothly bounded strongly pseudoconvex domain.

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The comparability of the Kobayashi approach region and the admissible approach region

Cited by 11 publications

References 0 publications

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\bf C}^2$

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\bf C}^2$

The Kobayashi balls of ( $${\mathbb {C}}$$ C -)convex domains

Some aspects of the Kobayashi and Carathéodory metrics on pseudoconvex domains

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