A WEIGHTED EXTREMAL FUNCTION AND EQUILIBRIUM MEASURE

We find an explicit formula for the weighted extremal function of ℝn ⊂ℂn with weight ${\left( {1 + x_1^2 + . + x_n^2} \right)^{ - 1/2}}$ as well as its Monge-Ampère measure. As a corollary, we compute the Alexander capacity of ℝℙn.

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Bibliographic Details
Published in:Mathematica scandinavica 2017-01, Vol.121 (2), p.243-262
Main Authors: BOS, LEN, LEVENBERG, NORMAN, MA'U, SIONE, PIAZZON, FEDERICO
Format: Article
Language:English
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Summary:We find an explicit formula for the weighted extremal function of ℝn ⊂ℂn with weight ${\left( {1 + x_1^2 + . + x_n^2} \right)^{ - 1/2}}$ as well as its Monge-Ampère measure. As a corollary, we compute the Alexander capacity of ℝℙn.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-26266