Acta Mathematica Vietnamica
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RELATIVE CAPACITY AND THE RELATIVE EXTREMAL FUNCTIONS UNDER HOLOMORPHIC COVERINGS
LE MAU HAI, TANG VAN LONGpp. 275-284
Abstract
In this note we establish formulas on the relative capacity of a subset $E$ in a domain $\Omega \subset \mathbb C^n$ for cases either $\Omega$ is pseudoconvex or $\Omega$ is hyperconvex and $E \subset \Omega$ is a closed subset such that $\overline{E}_{\mathbb C^n} \cap \partial \Omega$ is pluripolar. Moreover the relation between relative extremal functions in a generalized holomorphic covering is studied here.