Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Surfaces carrying sufficiently many Dirichlet finite harmonic functions that are automatically bounded
Mitsuru Nakai
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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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2012 Volume 64 Issue 1 Pages 201-229

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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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© 2012 The Mathematical Society of Japan
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