Displaying similar documents to “Two remarks on Riemann surfaces.”

Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.

José M. Rodríguez (1994)

Publicacions Matemàtiques

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We prove that if a Riemann surface has a linear isoperimetric inequality and verifies an extra condition of regularity, then there exists a non-constant harmonic function with finite Dirichlet integral in the surface. We prove too, by an example, that the implication is not true without the condition of regularity.

On the number of coincidences of morphisms between closed Riemann surfaces.

Yolanda Fuertes, Gabino González-Díez (1993)

Publicacions Matemàtiques

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We give a bound for the number of coincidence of two morphisms between given compact Riemann surfaces (complete complex algebraic curves). Our results generalize well known facts about the number of fixed points of an automorphism.

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.