Typical surfaces and random graphs
Robert Brooks (1998-1999)
Séminaire de théorie spectrale et géométrie
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Robert Brooks (1998-1999)
Séminaire de théorie spectrale et géométrie
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Rubén A. Hidalgo (2011)
Fundamenta Mathematicae
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Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S...
Izquierdo, Milagros, Singerman, David (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Costa, Antonio F., Izquierdo, Milagros (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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M. A. Magid (2004)
Annales Polonici Mathematici
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Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.
Bujalance, E., Costa, A.F., Singerman, D. (1993)
Annales Academiae Scientiarum Fennicae. Series A I. 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.
M. Lorens (1970)
Annales Polonici Mathematici
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G. Gromadzki, W. Marzantowicz (2011)
Fundamenta Mathematicae
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It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions...
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.
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...
Paul Schmutz (1994)
Manuscripta mathematica
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Arés Gastesi, Pablo (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)
Banach Center Publications
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We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.
José Bertin (1983)
Mathematische Annalen
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Mitsuru Nakai, Moses Glasner (1979)
Mathematische Zeitschrift
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Ngaiming Mok (1981)
Mathematische Annalen
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Ewa Kozłowska-Walania (2007)
Colloquium Mathematicae
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We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry...
Grzegorz Gromadzki (1990)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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