Porti, Joan
Regenerating hyperbolic cone 3-manifolds from dimension 2  [ Régénérescense des 3-variétés coniques hyperboliques dès la dimension 2 ]
Annales de l'institut Fourier, Tome 63 (2013) no. 5 , p. 1971-2015
MR 3186514 | Zbl 1293.57012
doi : 10.5802/aif.2820
URL stable : http://www.numdam.org/item?id=AIF_2013__63_5_1971_0

Classification:  57M50,  57N10
Mots clés: orbifold, 3-variété conique hyperbolique, dégénérescense, polygone hyperbolique, périmètre
On prouve qu’une 3-orbifold close qui fibre sur une 2-orbifold hyperbolique et polygonale admet une famille de structures coniques hyperboliques qu’on voit comme une régénérescence du polygone, pourvu que son périmètre soit minimal.
We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regenerations of the polygon, provided that the perimeter is minimal.

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