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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

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