Abstract
Let α(E) be the continuous analytic capacity of a compact set E ⊂ ℂ. In this paper we obtain a characterization of α in terms of curvature of measures with zero linear density, and we deduce that α is countably semiadditive. This result has important consequences for the theory of uniform rational approximation on compact sets. In particular, it implies the so-called inner boundary conjecture.
Original language | English |
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Pages (from-to) | 523-567 |
Journal | American Journal of Mathematics |
Volume | 126 |
Issue number | 3 |
Publication status | Published - 1 Jun 2004 |