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Proper periods of normal N.E.C. subgroups with even index.

Emilio Bujalance (1981)

Revista Matemática Hispanoamericana

By a non-Euclidean crystallographic (N.E.C.) group we shall mean a discrete subgroup Γ of isometries of the non-Euclidean plane including those reverse orientation, reflections and glide-reflections.In [1] we computed the proper periods of normal N.E.C. subgroups of an N.E.C. group, when the index of the group with respect to the subgroup is odd. In this paper we shall compute the proper period of normal N.E.C. subgroups, when the index is even.The corresponding problem for Fuchsian groups, which...

Pseudo-laplaciens II

Yves Colin de Verdière (1983)

Annales de l'institut Fourier

Dans cet article, nous étudions une famille d’opérateurs auto-adjoints Δ a dérivés du laplacien sur une surface de Riemann d’aire finie et ayant au voisinage de l’infini la structure d’un cylindre [ b , + [ × R / Z muni d’une métrique à courbure constante - 1 . Après avoir étudié la théorie spectrale de tels opérateurs, nous donnons, comme application, un théorème prévoyant l’absence générique de valeurs propres immergées dans le spectre continu du laplacien de ces surfaces. Nous montrons enfin comment ceci permet de...

Quasiconformal groups of compact type.

Petra Bonfert-Taylor, Gaven Martin (2005)

Revista Matemática Iberoamericana

We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.

Quasiconformal mappings of Y-pieces.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.

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