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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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Pairs of symmetries of Riemann surfaces.

Parabolic bundles, elliptic surfaces and SU (2)-representation spaces of genus zero Fuchsian groups.

Parameterizations of algebraic curves.

Parametrization of Möbius groups acting in a disk.

Parametrization of reflection groups acting in a disk.

Parametrization of the moduli space of hyperelliptic and symmetric Riemann surfaces.

Parity of the spin structure defined by a quadratic differential.

Period matrices of Accola-MacLachlan and Kulkarni surfaces.

Periodic automorphisms of surfaces: Invariant circles and maximal orders.

Periodic solitons and real algebraic curves.

Periods of harmonic Prym differentials on a compact Riemann surface.

Pleating coordinates for the Earle embedding

Poincaré series and holomorphic averaging.

Poincaré series and negatively curved manifolds.

Pointed $k$ -surfaces

Polyhedral Realization of a Thurston Compactification

Polymorphic Functions for Groups of Divergence Type.

Polynomial complexity of the Gilman-Maskit discreteness algorithm.

Polynomial invariants for fibered 3-manifolds and teichmüller geodesics for foliations

Presentation of hyperelliptic periodic monodromies and splitting families.

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