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Acta Mathematica Vietnamica

RELATIVE CAPACITY AND THE RELATIVE EXTREMAL FUNCTIONS UNDER HOLOMORPHIC COVERINGS

LE MAU HAI, TANG VAN LONG

Abstract

In this note we establish formulas on the relative capacity of a subset E in a domain ΩCn for cases either Ω is pseudoconvex or Ω is hyperconvex and EΩ is a closed subset such that ECnΩ is pluripolar. Moreover the relation between relative extremal functions in a generalized holomorphic covering is studied here.