A Characterization of Complex Manifolds Biholomorphic to a Circular Domain.
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Giorgio Patrizio (1985)
Mathematische Zeitschrift
Azimbay Sadullaev (2012)
Annales Polonici Mathematici
We consider a class of maximal plurisubharmonic functions and prove several properties of it. We also give a condition of maximality for unbounded plurisubharmonic functions in terms of the Monge-Ampère operator .
Zbigniew Błocki (1992)
Annales Polonici Mathematici
We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
Johan Thorbiörnson (1988)
Monatshefte für Mathematik
Giovanni Bassanelli (1994)
Forum mathematicum
Gregor Fels (1995)
Annales de l'institut Fourier
Let be a complex reductive group. We give a description both of domains and plurisubharmonic functions, which are invariant by the compact group, , acting on by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space . Such an invariant domain with a smooth boundary is Stein if and only if the corresponding domain is geodesically convex and the sectional curvature of its boundary fulfills the condition . The term is explicitly computable...
Urban Cegrell (2008)
Annales Polonici Mathematici
We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
Thomas Bloom, Norman Levenberg, Yu. Lyubarskii (2008)
Annales de l’institut Fourier
For a regular, compact, polynomially convex circled set in , we construct a sequence of pairs of homogeneous polynomials in two variables with
Urban Cegrell (1982)
Monatshefte für Mathematik
W. Plesniak (1995)
Monatshefte für Mathematik
Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
We prove that an analytic surface in a neighborhood of the origin in satisfies the local Phragmén-Lindelöf condition at the origin if and only if satisfies the following two conditions: (1) is nearly hyperbolic; (2) for each real simple curve in and each , the (algebraic) limit variety satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure -dimensional analytic variety to satisify .
Armen Edigarian (2003)
Annales Polonici Mathematici
We give a simplified proof of J. P. Rosay's result on plurisubharmonicity of the envelope of the Poisson functional [10].
Dieter Riebesehl, Friedmar Schulz (1984)
Mathematische Zeitschrift
Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class . This is done by establishing...
Rüdiger Braun, Reinhold Meise, B. Taylor (1999)
Annales Polonici Mathematici
For complex algebraic varieties V, the strong radial Phragmén-Lindelöf condition (SRPL) is defined. It means that a radial analogue of the classical Phragmén-Lindelöf Theorem holds on V. Here we derive a sufficient condition for V to satisfy (SRPL), which is formulated in terms of local hyperbolicity at infinite points of V. The latter condition as well as the extension of local hyperbolicity to varieties of arbitrary codimension are introduced here for the first time. The proof of the main result...
Sławomir Kołodziej (2003)
Annales Polonici Mathematici
regularity of the solutions of the complex Monge-Ampère equation in ℂPⁿ with the n-root of the right hand side in is proved.
Hai Mau Le, Hong Xuan Nguyen, Hung Viet Vu (2014)
Annales Polonici Mathematici
We prove a comparison principle for the log canonical threshold of plurisubharmonic functions under an assumption on complex Monge-Ampère measures.
T.J. Ransford (1993)
Mathematische Annalen
Nguyen Quang Dieu (2011)
Annales Polonici Mathematici
We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
Jerzy Kalina (1983)
Annales Polonici Mathematici
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