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Harmonic measure, infinite kernels,
and symmetrization


Author: John A. Velling
Journal: Proc. Amer. Math. Soc. 124 (1996), 3739-3743
MSC (1991): Primary 30C85
DOI: https://doi.org/10.1090/S0002-9939-96-03562-9
MathSciNet review: 1346991
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Abstract | References | Similar Articles | Additional Information

Abstract: The vanishing of area for the infinite Nielsen kernel of an arbitrary open Riemann surface is shown to follow from iteration of a natural geometric operation on the unit disk. This operation compares the distribution of harmonic measure on the boundaries of two related simply connected domains, and is not yet sufficiently well understood.


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

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  • 2. Cao, J., The Bers-Nielsen kernels and souls of open surfaces with negative curvature, Michigan Math. J. 41 (1994), 13-30. MR 95d:30085
  • 3. Haas, A., Linearization and mappings onto pseudocircle domains, Trans. AMS 282 (1984), 415-429. MR 86b:30069
  • 4. Halpern, N., On the infinite Nielsen extension of a torus, Comp. Var. 4 (1984), 111-117. MR 86b:30068
  • 5. -, Some remarks on Nielsen extensions of Riemann surfaces, Mich. Math. J. 30 (1983), 65-68. MR 84j:30079
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  • 7. -, Two theorems on Nielsen cores, Comp. Var. 8 (1987), 123-127. MR 88k:30053

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Additional Information

John A. Velling
Affiliation: Department of Mathematics, Brooklyn College (CUNY), Brooklyn, New York 11210
Email: jvelling@brooklyn.cuny.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03562-9
Received by editor(s): May 12, 1995
Additional Notes: Partially supported by NSF grant # 4401728 and PSC-CUNY grant #6-64131
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society

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