Geometric characterization of hyperelliptic Riemann surfaces.
Schmutz Schaller, Paul (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Schmutz Schaller, Paul (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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McShane, Greg (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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Parlier, Hugo (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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Aigon-Dupuy, Aline (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Hämenstadt, Ursula (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Hugo Parlier (2005)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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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.
Cooper, D., Long, D.D. (2001)
Geometry & Topology
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Cyril Lecuire (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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The bending map of a hyperbolic -manifold maps a convex cocompact hyperbolic metric on a -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.
Alex Eskin, Howard Masur, Anton Zorich (2003)
Publications Mathématiques de l'IHÉS
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A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description...