Displaying similar documents to “The higher topological form of Plateau's problem”

On ovals on Riemann surfaces.

Grzegorz Gromadzki (2000)

Revista Matemática Iberoamericana

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We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.

On commutativity and ovals for a pair of symmetries of a Riemann surface

Ewa Kozłowska-Walania (2007)

Colloquium Mathematicae

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We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry...

Koebe's general uniformisation theorem for planar Riemann surfaces

Gollakota V. V. Hemasundar (2011)

Annales Polonici Mathematici

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We give a complete and transparent proof of Koebe's General Uniformisation Theorem that every planar Riemann surface is biholomorphic to a domain in the Riemann sphere ℂ̂, by showing that a domain with analytic boundary and at least two boundary components on a planar Riemann surface is biholomorphic to a circular-slit annulus in ℂ.

Two remarks on Riemann surfaces.

José M. Rodriguez (1994)

Publicacions Matemàtiques

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We study the relationship between linear isoperimetric inequalities and the existence of non-constant positive harmonic functions on Riemann surfaces. We also study the relationship between growth conditions of length of spheres and the existence and the existence of Green's function on Riemann surfaces.

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.

Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations

Rubén A. Hidalgo (2011)

Fundamenta Mathematicae

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Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S...