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A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - S l o g | P | d σ ) : P a polynomial in n , where S denotes the euclidean unit sphere in n and σ its unitary surface measure.

A new characterization of the analytic surfaces in 3 that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that an analytic surface V in a neighborhood of the origin in 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in 3 and each d 1 , the (algebraic) limit variety T γ , d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k -dimensional analytic variety V to satisify PL loc .

A note on Rosay's paper

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].

A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties

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...

An energy estimate for the complex Monge-Ampère operator

Urban Cegrell, Leif Persson (1997)

Annales Polonici Mathematici

We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.

Bounded holomorphic functions with multiple sheeted pluripolar hulls

Armen Edigarian, Józef Siciak, Włodzimierz Zwonek (2006)

Studia Mathematica

We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.

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