On the solvability of monge-ampere type equations in non-uniformly convex domains.
N. Kutev (1991)
Mathematische Zeitschrift
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N. Kutev (1991)
Mathematische Zeitschrift
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Misha Bialy (1993)
Mathematische Zeitschrift
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Armen Edigarian (2004)
Annales Polonici Mathematici
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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
Moses Glasner (1971)
Mathematische Zeitschrift
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Nikolai Nikolov (2006)
Annales Polonici Mathematici
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We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
K. Srinivasacharyulu (1965)
Mathematische Zeitschrift
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Philip Hartman, Calvin Wilcox (1961)
Mathematische Zeitschrift
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Leon Brown, Jean-Pierre Kahane (1982)
Mathematische Annalen
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Gerd Schmalz (1989)
Mathematische Zeitschrift
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John K. Luedemann (1970)
Mathematische Zeitschrift
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O.T. O'Meara (1964/65)
Mathematische Zeitschrift
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Łukasz Kosiński, Tomasz Warszawski (2013)
Annales Polonici Mathematici
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In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.
Brackx, Freddy, Pincket, Willy
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