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Note on the Harmonic Measure of the Accessible Boundary of a Covering Riemann Surface

Published online by Cambridge University Press:  22 January 2016

Makoto Ohtsuka
Makoto Ohtsuka*
Affiliation:
Mathematical Institute, Nagoya University
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The following relation was set up in [5] for an open covering Riemann surface ℜ with positive boundary over an abstract Riemann surface

(1)

when the universal covering surface of the projection is not of hyperbolic type when is of hyperbolic type this relation is reduced to

(2)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 5 , February 1953 , pp. 35 - 38
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Evans, G.: Potentials and positively infinite singularities of harmonic functions, Monat. Math. Phys., 43 (1936), pp. 419–424.Google Scholar
[2] Hausdorff, F. : Mengenlehre, 3 Aufl., Berlin and Leipzig (1935).Google Scholar
[3] Nevanlinna, R. : Über die Lösbarkeit des Dirichletschen Problems für eine Riemannsche Fläche, Nachr. Gött., 1 (1938), pp. 181–193.Google Scholar
[4] Ohtsuka, M. : Dirichlet problems on Riemann surfaces and conformal mappings, Nagoya Math. Journ., 3 (1951), pp. 91–137.Google Scholar
[5] Ohtsuka, M. : On a covering surface over an abstract Riemann surface, Nagoya Math. Journ., 4 (1952), pp. 109–118.Google Scholar