Displaying similar documents to “Lengths of geodesics on Riemann surfaces with boundary.”

Continuity of the bending map

Cyril Lecuire (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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The bending map of a hyperbolic 3 -manifold maps a convex cocompact hyperbolic metric on a 3 -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.

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.