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A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

Navigating moduli space with complex twists

Curtis McMullen (2013)

Journal of the European Mathematical Society

We discuss a common framework for studying twists of Riemann surfaces coming from earthquakes, Teichmüller theory and Schiffer variations, and use it to analyze geodesics in the moduli space of isoperiodic 1-forms.

Nielsen's theorem and the super-Teichmüller space

P. Bryant, L. Hodgkin (1993)

Annales de l'I.H.P. Physique théorique

Non-rectifiable limit sets of dimension one.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3)...

Non-uniqueness of geodesics in infinite-dimensional Teichmüller spaces. II.

Li, Zhong (1993)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

On a distance defined by the length spectrum on Teichmüller space.

Shiga, Hiroshige (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

On Teichmüller modular forms.

Takashi Ichikawa (1994)

Mathematische Annalen

On the Bers fiber spaces.

Zhang, Chaohui (1999)

Annales Academiae Scientiarum Fennicae. Mathematica

On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces.

Stefano Trapani (1992)

Mathematische Annalen

On the shape of Bers-Maskit slices.

Komori, Yohei, Parkkonen, Jouni (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

On the tangent space to the universal Teichmüller space.

Nag, Subhashis (1993)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

Orbifold Riemann surfaces and the Yang-Mills-Higgs equations

Ben Nasatyr, Brian Steer (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Pleating coordinates for the Earle embedding

Yohei Komori, Caroline Series (2001)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Pointed $k$ -surfaces

Graham Smith (2006)

Bulletin de la Société Mathématique de France

Let $S$ be a Riemann surface. Let $ℍ^{3}$ be the $3$ -dimensional hyperbolic space and let $\partial_{\infty} ℍ^{3}$ be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping $ϕ : S \to \partial_{\infty} ℍ^{3} = \hat{ℂ}$ . If $i : S \to ℍ^{3}$ is a convex immersion, and if $N$ is its exterior normal vector field, we define the Gauss lifting, $\hat{ı}$ , of $i$ by $\hat{ı} = N$ . Let $\vec{n} : U ℍ^{3} \to \partial_{\infty} ℍ^{3}$ be the Gauss-Minkowski mapping. A solution to the Plateau problem $(S, ϕ)$ is a convex immersion $i$ of constant Gaussian curvature equal to $k \in (0, 1)$ such that the Gauss lifting $(S, \hat{ı})$ is complete and $\vec{n} \circ \hat{ı} = ϕ$ . In this paper, we show...

Polyhedral Realization of a Thurston Compactification

Matthieu Gendulphe, Yohei Komori (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Let $Σ_{3}^{-}$ be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space $Teich (Σ_{3}^{-})$ as a simplex in $P (ℝ^{4})$ .

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