Characterizations of boundary pluripolar Hulls

We present some basic properties of the boundary relative extremal function and discuss so called boundary pluripolar sets and boundary pluripolar hulls. We show that for B-regular domains the boundary pluripolar hull is always trivial on the boundary of the domain and present a "boundary version" of Zeriahi's theorem on the completeness of pluripolar sets.Comment: 9 pages, In this version some small changes were made and a few typo's were corrected. Version 3 has 10 pages. Section 2 has been rewritten. It now includes observations about different versions of the boundary extremal function as introduced by Sadullaev. We removed superfluous assumptions in some of the statement