Charakteryzacja brzegowych otoczek pluripolarnych

Bibliogr. s. 47-52

A pluripolar set in a domain D is a subset of D that lies in -locus of a plurisubharmonic function in D: Some properties and applications of such a set are known. In this thesis we will discuss boundary pluripolar set and hull. A set in D is called boundary pluripolar or b - pluripolar for D if it is a subset of -locus of an upper semicontinuous function on that is plurisubharmonic in D. We will discuss different possibilities to compute boundary pluripolar hull of a b-pluripolar set in the boundary of a domain. We give some properties of boundary relative extremal function and use it to characterize boundary pluripolar hull in the domain. We show the existence of a set that is b-pluripolar for the unit ball but not pluripolar in . We prove by two different methods that the hull is always trivial in the boundary of a B-regular domain. After giving some approximation theorems of holomorphic maps we characterize boundary pluripolar sets in terms of analytic disc. We review the definitions of the boundary relative extremal: For various domains we give an affirmative answer to the question of Sadullaev, [71], whether these extremal functions are equal. We also show that certain versions of Edwards duality theorem do not hold in open sets. By using Poletsky's theory we characterize the thinness of a subset in by analytic discs.