Analytic capacity , rectifiability , and the Cauchy integral

  title={Analytic capacity , rectifiability , and the Cauchy integral},
  author={Xavier Tolsa},
A compact set E ⊂ C is said to be removable for bounded analytic functions if for any open set containing E, every bounded function analytic on \ E has an analytic extension to . Analytic capacity is a notion that, in a sense, measures the size of a set as a non removable singularity. In particular, a compact set is removable if and only if its analytic capacity vanishes. The so-called Painlevé problem consists in characterizing removable sets in geometric terms. Recently many results in… CONTINUE READING
Highly Cited
This paper has 27 citations. REVIEW CITATIONS

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
21 Extracted Citations
76 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 76 references


  • A. Volberg, Calderón-Zygmund capacities, operators on nonhomogeneous spaces. CBMS Regional Conf. Ser. Math
  • Amer. Math. Soc., Providence, RI,
  • 2003
Highly Influential
5 Excerpts

The Geometric Traveling Salesman Problem in the Heisenberg Group

  • F. Ferrari, B. Franchi, H. Pajot
  • Preprint,
  • 2005
Highly Influential
2 Excerpts


  • G. David, S. Semmes, Analysis of, on uniformly rectifiable sets. Math. Surveys Monogr
  • Amer. Math. Soc., Providence, RI,
  • 1993
Highly Influential
3 Excerpts

Menger curvature and Lipschitz parametrizations in metric spaces

  • I. Hah I. Hahlomaa
  • Fund. Math
  • 2005

Similar Papers

Loading similar papers…