### Counting immersed surfaces in hyperbolic 3-manifolds.

Masters, Joseph D. (2005)

Algebraic & Geometric Topology

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Masters, Joseph D. (2005)

Algebraic & Geometric Topology

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Mohanty, Yana (2003)

Algebraic & Geometric Topology

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Francisco Perdomo, Ángel Plaza (2014)

Open Mathematics

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The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the...

Bachman, David, Cooper, Daryl, White, Matthew E. (2004)

Algebraic & Geometric Topology

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Marica Šarac (1997)

Matematički Vesnik

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Dowty, James G. (2002)

Algebraic & Geometric Topology

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François Fillastre (2007)

Annales de l’institut Fourier

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A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly...

Milica Stojanović (1997)

Matematički Vesnik

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Hruska, G.Christopher (2004)

Geometry & Topology

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Carlo Petronio (2000)

Bollettino dell'Unione Matematica Italiana

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Quello delle triangolazioni geodetiche ideali è un metodo molto potente per costruire strutture iperboliche complete di volume finito su 3-varietà non compatte, ma non è noto se il metodo sia applicabile in generale. È tuttavia noto che esistono triangolazioni ideali parzialmente piatte, ma l'analisi della situazione diviene più ardua sotto diversi aspetti, quando si ha a che fare con tetraedri piatti oltre che veri tetraedri. In particolare, la topologia dello spazio di identificazione...