In: Aequationes mathematicae, 2014, vol. 88, no. 1-2, p. 199-200
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In: Aequationes mathematicae, 2013, vol. 85, no. 3, p. 449-463
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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.
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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.
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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.
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In: Canadian Journal of Mathematics
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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...
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