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

Ewa Kozłowska-Walania

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Displaying similar documents to “On commutativity and ovals for a pair of symmetries of a Riemann surface”

On pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska (2005)

Colloquium Mathematicae

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A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of...

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 the connectedness of the locus of real Riemann surfaces.

Costa, Antonio F., Izquierdo, Milagros (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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Hyperelliptic maps and surfaces

David Singerman (1997)

Mathematica Slovaca

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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.

The higher topological form of Plateau's problem

Jesse Douglas (1939)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Riemann surface of a uniform dessin.

Singerman, David, Syddall, Robert I. (2003)

Beiträge zur Algebra und Geometrie

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Riemann problem on the double of a multiply connected circular region

V. V. Mityushev (1997)

Annales Polonici Mathematici

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The Riemann problem has been solved in [9] for an arbitrary closed Riemann surface in terms of the principal functionals. This paper is devoted to solution of the problem only for the double of a multiply connected region and can be treated as complementary to [9,1]. We obtain a complete solution of the Riemann problem in that particular case. The solution is given in analytic form by a Poincaré series.

On supersoluble groups acting on Klein surfaces.

Grzegorz Gromadzki (1990)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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On trigonal Riemann surfaces with non-unique morphims

Daniel Ying (2005)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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Non-maximal cyclic group actions on compact Riemann surfaces.

David Singerman, Paul Watson (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We say that a finite group G of automorphisms of a Riemann surface X is non-maximal in genus g if (i) G acts as a group of automorphisms of some compact Riemann surface Xg of genus g and (ii), for all such surfaces Xg , |Aut Xg| > |G|. In this paper we investigate the case where G is a cyclic group Cn of order n. If Cn acts on only finitely many surfaces of genus g, then we completely solve the problem of finding all such pairs (n,g).