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Pluripolarity of sets with small Hausdorff measure

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Abstract:

We show that any set E⊂C 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.

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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, Canberra 0200 ACT, Australia. e-mail: labutin@maths.anu.edu.au, , , , , , AU

    Denis A. Labutin

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  1. Denis A. Labutin
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Received: 20 May 1999

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Labutin, D. Pluripolarity of sets with small Hausdorff measure. manuscripta math. 102, 163–167 (2000). https://doi.org/10.1007/s002291020163

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  • DOI: https://doi.org/10.1007/s002291020163

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