The Bergman Kernel on Uniformly Extendable Pseudoconvex Domains.
Takeo Ohsawa, Klaus Diederich, Gregor Herbort (1985/86)
Mathematische Annalen
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The Bergman Kernel on Uniformly Extendable Pseudoconvex Domains.
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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...
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Estimation of the Carathéodory distance on pseudoconvex domains of finite type whose boundary has Levi form of corank at most one
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...