Painlevé’s Problem and the Semiadditivity of Analytic Capacity
نویسنده
چکیده
Let γ(E) be the analytic capacity of a compact set E and let γ+(E) be the capacity of E originated by Cauchy transforms of positive measures. In this paper we prove that γ(E) ≈ γ+(E) with estimates independent of E. As a corollary, we characterize removable singularities for bounded analytic functions in terms of curvature of measures, and we deduce that γ is semiadditive.
منابع مشابه
Painlevé’s Problem and the Semiadditivity of Analytic Capacity
Let γ(E) be the analytic capacity of a compact set E and let γ+(E) be the capacity of E originated by Cauchy transforms of positive measures. In this paper we prove that γ(E) ≈ γ+(E) with estimates independent of E. As a corollary, we characterize removable singularities for bounded analytic functions in terms of curvature of measures, and we deduce that γ is semiadditive.
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