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manuscripta mathematica

, Volume 102, Issue 2, pp 163–167 | Cite as

Pluripolarity of sets with small Hausdorff measure

  • Denis A. Labutin

Abstract:

We show that any set EC n , n≥ 2, with finite Hausdorff measure¶\(\) is pluripolar. The result is sharp with respect to the measuring function. The new idea in the proof is to combine a construction from potential theory, related to the real variational integral \(\), \(\), with properties of the pluricomplex relative extremal function for the Bedford–Taylor capacity.

Mathematics Subject Classification (1991):32F05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Denis A. Labutin
    • 1
  1. 1.Centre for Mathematics and its Applications, Australian National University, Canberra 0200 ACT, Australia. e-mail: labutin@maths.anu.edu.auAU

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