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Displaying similar documents to “Surfaces of minimum capacity for a knot”

Crosscaps and knots.

Clark, Bradd Evans (1978)

International Journal of Mathematics and Mathematical Sciences

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An indestructible Blaschke product in the little Bloch space.

Christopher J. Bishop (1993)

Publicacions Matemàtiques

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The little Bloch space, B, is the space of all holomorphic functions f on the unit disk such that lim lf'(z)l (1- lzl) = 0. Finite Blaschke products are clearly in B, but examples of infinite products in B are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others). Stephenson has asked whether B contains an infinite, indestructible Blaschke product, i.e., a Blaschke product B so that (B(z) - a)/(1 - âB(z)), is also a Blaschke...

Harmonic morphisms onto Riemann surfaces and generalized analytic functions

Paul Baird (1987)

Annales de l'institut Fourier

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We study harmonic morphisms from domains in R 3 and S 3 to a Riemann surface N , obtaining the classification of such in terms of holomorphic mappings from a covering space of N into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of S 3 to a Riemann surface is essentially the Hopf map. Comparison is made with the theory of analytic functions. In particular we consider multiple-valued harmonic morphisms defined on domains...

Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi (1976)

Annales de l'institut Fourier

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We considerably improve our earlier results [Ann. Inst. Fourier, 24-4 (1974] concerning Cauchy-Read’s theorems, convergence of Green lines, and the structure of invariant subspaces for a class of hyperbolic Riemann surfaces.