Determination of the pluripolar hull of graphs of certain holomorphic functions

Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> be a closed polar subset of a domain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>D</mml:mi> </mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℂ</mml:mi> </mml:math> . We give a complete description of the pluripolar hull <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>×</mml:mo> <mml:mi>ℂ</mml:mi> </mml:mrow> <mml:mo>*</mml:mo> </mml:msubsup> </mml:math> of the graph <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> of a holomorphic function defined on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>∖</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> . To achieve this, we prove for pluriharmonic measure certain semi-continuity properties and a localization principle.

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