Estimates of the Bergman kernel function on certain pseudoconvex domains in Cn.
Sanghyun Cho (1996)
Mathematische Zeitschrift
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Sanghyun Cho (1996)
Mathematische Zeitschrift
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Joachim Michel (1993)
Mathematische Zeitschrift
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Gregor Herbort (2013)
Annales Polonici Mathematici
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We study the class of smooth bounded weakly pseudoconvex domains D ⊂ ℂⁿ whose boundary points are of finite type (in the sense of J. Kohn) and whose Levi form has at most one degenerate eigenvalue at each boundary point, and prove effective estimates on the invariant distance of Carathéodory. This completes the author's investigations on invariant differential metrics of Carathéodory, Bergman, and Kobayashi in the corank one situation and on invariant distances on pseudoconvex finite...
Takeo Ohsawa, Klaus Diederich, Gregor Herbort (1985/86)
Mathematische Annalen
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R. Michael Range (1990)
Mathematische Annalen
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Gregor Herbort (1992)
Mathematische Zeitschrift
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Andrei Iordan (1984/85)
Mathematische Zeitschrift
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Ewa Ligocka (1981)
Annales Polonici Mathematici
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Włodzimierz Zwonek
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Our work is divided into five chapters. In Chapter I we introduce necessary notions and we present the most important facts that we shall use. We also present our main results. Chapter I covers the following topics: • holomorphically contractible families of functions and pseudometrics, their basic properties, product property, Lempert Theorem, notion of geodesic, problem of finding effective formulas for invariant functions and pseudometrics and geodesics, completeness...
Włodzimierz Zwonek (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Klas Diederich, John Eric Fornaess (1980)
Mathematische Annalen
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Steven R. Bell, Harold P. Boas (1981)
Mathematische Annalen
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Prachi Mahajan (2012)
Annales Polonici Mathematici
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This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between...
N. Watts Gebelt (1995)
Mathematische Zeitschrift
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