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Sario’s Potentials and Analytic Mappings*
Published online by Cambridge University Press: 22 January 2016
Extract
In order to extend Nevanlinna’s first and second fundamental theorems to arbitrary analytic mappings between Riemann surfaces, Sario [8, 9] introduced a kernel function on an arbitrary Riemann surface generalizing the elliptic kernel on the Riemann sphere. Because of the importance of the potential theoretic method in the value distribution theory, we discussed potentials of Sario’s kernel in [4]. In that paper the validty of Frostman’s maximum principle for Sario’s potentials was left unsettled. The main object of this paper is to resolve this question (Theorem 1). As a consequence the fundamental theorem of the potential theory is obtained in its complete form for Sario’s potentials (Theorem 2).
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1967
Footnotes
The work was sponsored by the U.S. Army Research Office Durham, Grant DA-AROD-31-124-G 742, University of California, Los Angeles.
References
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