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Proceedings of the American Mathematical Society

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An estimate on the distortion
of the logarithmic capacity

Author: María J. González
Journal: Proc. Amer. Math. Soc. 126 (1998), 1429-1431
MSC (1991): Primary 30C85, 30F35
MathSciNet review: 1443154
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\Gamma$ be a Fuchsian group. We show that the existence of a set on $\partial \mathbb{D}$ with no $\Gamma$-equivalent points and positive logarithmic capacity does not imply that $\Gamma$ is of convergence type.

References [Enhancements On Off] (What's this?)

  • [C] L. Carleson, ``Selected Problems in Exceptional Sets", Van Nostrand-Reinhold, Princeton, NJ, 1967. MR 37:1576
  • [P] C. Pommerenke, On the Green's Fundamental Domain, Math. Z. 156 (1977), 157-164. MR 57:3382

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Additional Information

María J. González
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Spain
Address at time of publication: Departamento de Matemàtices, CASEM, Universidad de Cádiz, 11519 Puerto Real, Cádiz, Spain

Keywords: Fuchsian groups, harmonic measure, logarithmic capacity
Received by editor(s): October 21, 1996
Additional Notes: Research supported by DGICYT Grant PB92-0804-C02-02 and by CIRIT grant GRQ94-2014, Spain.
Communicated by: Linda Keen
Article copyright: © Copyright 1998 American Mathematical Society

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