Involutions and simple closed geodesics on 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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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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McShane, Greg (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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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.
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...
Maher, Joseph (2005)
Geometry & Topology
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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...
Hugo Parlier (2005)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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Costa, Antonio F., Izquierdo, Milagros (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Hämenstadt, Ursula (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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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.