Displaying similar documents to “How to prove Fefferman's theorem without use of differential geometry”

Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions

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...

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...

The Bergman kernel functions of certain unbounded domains

Friedrich Haslinger (1998)

Annales Polonici Mathematici

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We compute the Bergman kernel functions of the unbounded domains Ω p = ( z ' , z ) ∈ ℂ ² : z > p ( z ' ) , where p ( z ' ) = | z ' | α / α . It is also shown that these kernel functions have no zeros in Ω p . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.