Discs in pseudoconvex domains.
Franc Forstneric, Josip Globevnik (1992)
Commentarii mathematici Helvetici
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Franc Forstneric, Josip Globevnik (1992)
Commentarii mathematici Helvetici
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John Erik Fornaess, Eric Bedford (1978)
Inventiones mathematicae
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Takeo Ohsawa (2007)
Annales Polonici Mathematici
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In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained...
Andrei Iordan (1984/85)
Mathematische Zeitschrift
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Eric Bedford, Jiri Dadok (1987)
Commentarii mathematici Helvetici
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Klas Diederich, John Erik Fornaess (1982)
Manuscripta mathematica
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Mechthild Behrens (1985)
Mathematische Annalen
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Joachim Michel (1993)
Mathematische Zeitschrift
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Adib A. Fadlalla (1994)
Mathematische Annalen
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Akira Sakai (1982)
Mathematische Annalen
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William S. Cohn (1993)
Mathematica Scandinavica
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Franc Forstneric (1993)
Mathematische Zeitschrift
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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...
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...
J.E. Fornaess, K. Diederich (1977)
Inventiones mathematicae
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