Consortium of Swiss Academic Libraries

Scissors Congruence, the Golden Ratio and Volumes in Hyperbolic 5-Space

Kellerhals, Ruth

In: Discrete & Computational Geometry, 2012, vol. 47, no. 3, p. 629-658

Université de Fribourg

The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space

Kellerhals, Ruth ; Nonaka, Jun

In: Tokyo Journal of Mathematics, 2017, vol. 40, no. 2, p. 379–391

In [7], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by compact hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture holds in the context of ideal Coxeter polyhedra in H3. Our methods allow us to bound from below the growth rates of composite ideal Coxeter polyhedra by the growth rates of its ideal Coxeter polyhedral...

Université de Fribourg

Commensurability of hyperbolic Coxeter groups: theory and computation

Guglielmetti, Rafael ; Jacquemet, Matthieu ; Kellerhals, Ruth

In: RIMS Kôkyûroku Bessatsu, 2017, vol. B66, p. 057-113

For hyperbolic Coxeter groups of finite covolume we review and present new theoretical and computational aspects of wide commensurability. We discuss separately the arithmetic and the non-arithmetic cases. Some worked examples are added as well as a panoramic viewto hyperbolic Coxeter groups and their classification.

Université de Fribourg

On minimal covolume hyperbolic lattices

Kellerhals, Ruth

In: Mathematics, 2017, vol. 5, no. 3, p. 43

We study lattices with a non-compact fundamental domain of small volume in hyperbolic space H n . First, we identify the arithmetic lattices in Isom + H n of minimal covolume for even n up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for n = 11 and n = 13 in terms of the rotation subgroup of certain Coxeter pyramid groups found by Tumarkin. The ...

Université de Fribourg

On commensurable hyperbolic Coxeter groups

Guglielmetti, Rafael ; Jacquemet, Matthieu ; Kellerhals, Ruth

In: Geometriae Dedicata, 2016, vol. 183, no. 1, p. 143–167

For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions.

Université de Fribourg

Hyperbolic orbifolds of minimal volume

Kellerhals, Ruth

In: Computational Methods and Function Theory, 2014, p. 1–17

We provide a survey of hyperbolic orbifolds of minimal volume, starting with the results of Siegel in two dimensions and with the contributions of Gehring, Martin and others in three dimensions. For higher dimensions, we summarise some of the most important results, due to Belolipetsky, Emery and Hild, by discussing related features such as hyperbolic Coxeter groups, arithmeticity and...

Université de Fribourg

Scissors congruence, the golden ratio and volumes in hyperbolic 5-space

Kellerhals, Ruth

In: Discrete & Computational Geometry, 2012, vol. 47, no. 3, p. 629-658