Extension of Positive Currents with Special Properties of Monge-Ampère Operators

Authors

  • Ahmad L. al Abdulaali

DOI:

https://doi.org/10.7146/math.scand.a-15484

Abstract

In this paper we study the extension of currents across small obstacles. Our main results are: 1) Let A be a closed complete pluripolar subset of an open subset Ω of Cn and T be a negative current of bidimension (p,p) on ΩA such that ddcTS on ΩA for some positive plurisubharmonic current S on Ω. Assume that the Hausdorff measure H2p(A¯SuppT)=0. Then ˜T exists. Furthermore, the current R=~ddcTddc˜T is negative supported in A. 2) Let u be a positive strictly k-convex function on an open subset Ω of Cn and set A={zΩ:u(z)=0}. Let T be a negative current of bidimension (p,p) on ΩA such that ddcTS on ΩA for some positive plurisubharmonic (or ddc-negative) current S on Ω. If pk+1, then ˜T exists. If pk+2, ddcS0 and u of class C2, then ~ddcT exists and ~ddcT=ddc˜T.

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Published

2013-09-01

How to Cite

Abdulaali, A. L. al. (2013). Extension of Positive Currents with Special Properties of Monge-Ampère Operators. MATHEMATICA SCANDINAVICA, 113(1), 108–127. https://doi.org/10.7146/math.scand.a-15484

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Articles