Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Laszló Lempert (1983)
Mathematische Annalen
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Laszló Lempert (1983)
Mathematische Annalen
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Kunio Kakié (1985/86)
Mathematische Annalen
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Slimane Benelkourchi (2014)
Annales Polonici Mathematici
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We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
Urban Cegrell (1984)
Mathematische Zeitschrift
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Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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David Monn (1986)
Mathematische Annalen
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U. Pinkall, A. Schwenk-Schellschmidt (1994)
Mathematische Annalen
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John Erik Fornaess, Eric Bedford (1978/79)
Inventiones mathematicae
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Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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Björn Ivarsson (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
Rafał Czyż, Lisa Hed (2008)
Annales Polonici Mathematici
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We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.
John I.E. Urbas (1988)
Mathematische Zeitschrift
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László Lempert, Róbert Szöke (1991)
Mathematische Annalen
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Szymon Pliś (2005)
Annales Polonici Mathematici
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We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.
Urban Cegrell (1986)
Mathematische Zeitschrift
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Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Friedmar Schulz (1983)
Mathematische Annalen
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Nguyen Quang Dieu (2011)
Annales Polonici Mathematici
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We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
Pham Hoang Hiep (2005)
Annales Polonici Mathematici
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We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.