Surfaces carrying sufficiently many Dirichlet finite harmonic functions that are automatically bounded

Mitsuru NAKAI

doi:10.2969/jmsj/06410201

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Home > Journals > J. Math. Soc. Japan > Volume 64 > Issue 1 > Article

January, 2012 Surfaces carrying sufficiently many Dirichlet finite harmonic functions that are automatically bounded

Mitsuru NAKAI

J. Math. Soc. Japan 64(1): 201-229 (January, 2012). DOI: 10.2969/jmsj/06410201

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Abstract

It is shown that there exists a Riemann surface on which every Dirichlet finite harmonic function is automatically bounded and yet the linear dimension of the linear space of Dirichlet finite harmonic functions on it is infinite.

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Mitsuru NAKAI. "Surfaces carrying sufficiently many Dirichlet finite harmonic functions that are automatically bounded." J. Math. Soc. Japan 64 (1) 201 - 229, January, 2012. https://doi.org/10.2969/jmsj/06410201

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Published: January, 2012

First available in Project Euclid: 26 January 2012

zbMATH: 1264.30027

MathSciNet: MR2879742

Digital Object Identifier: 10.2969/jmsj/06410201

Subjects:

Primary: 30F20

Secondary: 30F15 , 30F25 , 31A15

Keywords: anticonformal pasting , capacity , Dirichlet finite , essentially positive , grafted surface , harmonic measure , Hyperbolic , parabolic‎ , quasibounded , Royden harmonic boundary , Sario-Tôki disc , Wiener harmonic boundary

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J. Math. Soc. Japan

Vol.64 • No. 1 • January, 2012

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Mitsuru NAKAI "Surfaces carrying sufficiently many Dirichlet finite harmonic functions that are automatically bounded," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 64(1), 201-229, (January, 2012)

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