A C2-estimate for solutions of complex Monge-Ampère equations.
A constant in pluripotential theory
We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
A Counterexample to the Strong Subadditivity of Extremal Plurisubharmonic Functions.
A Local Property of L-regular Sets.
A Local Version of Levenberg's Theorem on Determining Measures and Leja's Polynomial Condition.
A new characterization of the analytic surfaces in that satisfy the local Phragmén-Lindelöf condition
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 .
A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition
For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition it is shown that for each real simple curve γ and each d ≥ 1 the limit variety satisfies the strong Phragmén-Lindelöf condition (SPL).
A note on Rosay's paper
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
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...
A variational characterization of condenser capacities in within a class of plurisubharmonic functions
An energy estimate for the complex Monge-Ampère operator
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.
An extremal plurisubharmonic function associated to a convex pluricomplex Green function with pole at infinity.
Analytic discs method in complex analysis [Book]
Applications polynomiales et applications entières dans les espaces vectoriels topologiques
Associated families of pluriharmonic maps and isotropy.
Asymptotic behavior of Fourier-Laplace transform
Behaviour at the boundary of the complex Monge-Ampère equation
Biholomorphic invariance of capacity and the capacity of an annulus
Boundary estimates for derivatives of harmonic functions
Bounded holomorphic functions with multiple sheeted pluripolar hulls
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.