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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David Monn (1986)
Mathematische Annalen
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John I.E. Urbas (1988)
Mathematische Zeitschrift
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Kantorovich, L.V. (2004)
Journal of Mathematical Sciences (New York)
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U. Pinkall, A. Schwenk-Schellschmidt (1994)
Mathematische Annalen
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Pit-Mann Wong (1982)
Inventiones mathematicae
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Machida, Y., Morimoto, T. (1999)
Lobachevskii Journal of Mathematics
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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.
Eric Bedford (1982)
Mathematische Annalen
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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.
Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
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Sławomir Kołodziej (1996)
Annales Polonici Mathematici
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We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
Urban Cegrell (1986)
Mathematische Zeitschrift
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Jonas Wiklund (2004)
Annales Polonici Mathematici
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We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.
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.
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.