Characterizations of boundary pluripolar Hulls

TL;DR

This paper explores the properties of boundary pluripolar hulls and related extremal functions, establishing conditions under which these hulls are trivial and extending Zeriahi's theorem to boundary contexts.

Contribution

It introduces a boundary version of Zeriahi's theorem and characterizes boundary pluripolar hulls in B-regular domains, advancing understanding of pluripolar set behavior at boundaries.

Findings

Boundary pluripolar hulls are trivial on the boundary of B-regular domains.

A boundary version of Zeriahi's theorem is established.

Properties of boundary relative extremal functions are characterized.

Abstract

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.