Painleve's problem and the semiadditivity of analytic capacity
| dc.creator | Tolsa, Xavier | |
| dc.date | 2002-04-02 | |
| dc.date.accessioned | 2026-07-07T04:47:24Z | |
| dc.date.available | 2026-07-07T04:47:24Z | |
| dc.description | 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 $γ(E)\approxγ_+(E)$ 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, which solves a long standing question of Vitushkin. | |
| dc.description | 42 pages | |
| dc.identifier | https://arxiv.org/abs/math/0204027 | |
| dc.identifier | http://arxiv.org/abs/math/0204027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63697 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 30C85; 42B20 | |
| dc.title | Painleve's problem and the semiadditivity of analytic capacity | |
| dc.type | text |