Consortium of Swiss Academic Libraries

Erratum to: Volume of a doubly truncated hyperbolic tetrahedron

Kolpakov, Alexander ; Murakami, Jun

In: Aequationes mathematicae, 2014, vol. 88, no. 1-2, p. 199-200

Consortium of Swiss Academic Libraries

Volume of a doubly truncated hyperbolic tetrahedron

Kolpakov, Alexander ; Murakami, Jun

In: Aequationes mathematicae, 2013, vol. 85, no. 3, p. 449-463

Université de Fribourg

Volume of a doubly truncated hyperbolic tetrahedron

Kolpakov, Alexander ; Murakami, Jun

In: Aequationes mathematicae, 2013, vol. 85, no. 3, p. 449–463

he present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

Université de Fribourg

Examples of rigid and flexible seifert fibred cone-manifolds

Kolpakov, Alexander

In: Glasgow Mathematical Journal, 2013, vol. 55, no. 02, p. 411–429

The present paper gives an example of a rigid spherical cone-manifold and that of a flexible one, which are both Seifert fibred.

Université de Fribourg

On the optimality of the ideal right-angled 24-cell

Kolpakov, Alexander

In: Algebraic & Geometric Topology, 2012, vol. 12, p. 1941-1960

We prove that among four-dimensional ideal right-angled hyperbolic polytopes the 24–cell is of minimal volume and of minimal facet number. As a corollary, a dimension bound for ideal right-angled hyperbolic polytopes is obtained.

Université de Fribourg

Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

Kolpakov, Alexander

In: European Journal of Combinatorics, 2012, vol. 33, no. 8, p. 1709–1724

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a certain geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several...