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

Mitsuru Nakai

doi:10.2969/jmsj/06410201

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

著者情報

キーワード: anticonformal pasting, capacity, Dirichlet finite, essentially positive, grafted surface, harmonic measure, hyperbolic, parabolic, quasibounded, Royden harmonic boundary, Sario-Tôki disc, Wiener harmonic boundary

ジャーナルフリー

2012 年 64 巻 1 号 p. 201-229

DOI https://doi.org/10.2969/jmsj/06410201

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抄録

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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Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki

Tokyo Sugaku-Buturigakkwai Kizi Dai 2 Ki

Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo

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