On definitions of the pluricomplex Green function
We give several definitions of the pluricomplex Green function and show their equivalence.
On -harmonic space .
On M-harmonic space Bsp
On perturbations of pluriregular sets generated by sequences of polynomial maps
It is shown that an infinite sequence of polynomial mappings of several complex variables, with suitable growth restrictions, determines a filled-in Julia set which is pluriregular. Such sets depend continuously and analytically on the generating sequences, in the sense of pluripotential theory and the theory of set-valued analytic functions, respectively.
On series of homogeneous polynomials and their partial sums
On Stein manifolds M for which 0 (M) is somorphic to ... as Fréchet spaces.
On symmetry of the pluricomplex Green function for ellipsoids
We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
On the domains of existence for plurisubharmonic functions
On the equivalence between locally polar and globally polar sets in
On the movement of the Poincaré metric with the pseudoconvex deformation of open Riemann surfaces.
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the radius of convergence of an entire function in a normed space
Order functions of plurisubharmonic functions
We consider the following problem: find on a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on which is constant outside a polar set is the order function of a plurisubharmonic function.
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