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A weighted extremal function and equilibrium measure

Len Bos, Norman Levenberg, Sione Ma'u, Federico Piazzon


We find an explicit formula for the weighted extremal function of $\mathbb{R}^n\subset \mathbb{C}^n$ with weight $(1+x_1^2+\cdots +x_n^2)^{-1/2}$ as well as its Monge-Ampère measure. As a corollary, we compute the Alexander capacity of $\mathbb{RP}^n$.

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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