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Harmonic measure, infinite kernels, and symmetrization

Author(s): John A. Velling
Journal: Proc. Amer. Math. Soc. 124 (1996), 3739-3743.
MSC (1991): Primary 30C85
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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:

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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
6.: -, A theorem on infinite Nielsen extensions, Proc. AMS 97 (1986), 459-462. MR 88h:32017
7.: -, Two theorems on Nielsen cores, Comp. Var. 8 (1987), 123-127. MR 88k:30053


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