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Applications of Extremal Length to Classification of Riemann Surfaces

Published online by Cambridge University Press:  22 January 2016

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Let D be a subregion of a Riemann surface F, whose relative boundary consists of at most countable number of analytic curves which do not cluster in F. For a regular exhaustion {Fn} of F, we put Dn = D∩ (F— Fn), and define the extremal radius R(P, ∂Dn) of the relative boundary ∂Dn of Dn, measured at a point P(∈F0) of F with respect to the connected component of F - Dn which contains P. Let K(|z|≦r) be a disk centered at P and contained in a parametric disk of P.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1964

References

[1] Kuramochi, Z.. Singular points of Riemann surfaces, J. Fac. Sci. Hokkaido Univ. Ser. I vol. XVI. (1962) pp. 80148.Google Scholar
[2] Strebel, K.. Die Extremale Distanz zweier Enden einer Riemannschen Fläche, Ann. Acad. Sci. Fennicae., A.I. 179 (1955) pp. 121.Google Scholar
[3] Wolontis, V.. Properties of conformal invariants, Amer. J. Math. LXXIV. (1952) pp. 587606.Google Scholar