Publications

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Preprints R. Kellerhals, A polyhedral approach to the arithmetic and geometry of hyperbolic chain link complements, J. Knot Theory Ramifications 32 (2023), Paper No. 2350052, 24 pp. Publications S. T. Drewitz, R. Kellerhals, The non-arithmetic cusped hyperbolic 3-orbifold of minimal volume, Trans. Amer. Math. Soc. 376 (2023), 3819-3866. E. Dotti, S. T. Drewitz, R. Kellerhals, Cusp density and commensurability of non-arithmetic hyperbolic Coxeter orbifolds, Discrete Comput. Geom. 69 (2023), 873-895. R. Kellerhals, L. Liechti, Salem numbers, spectral radius and growth rates of hyperbolic Coxeter groups, Transformation Groups 28 (2023), 831-852. M. Conder, R. Kellerhals, Small volume hyperbolic manifolds constructed from Coxeter groups, Bull. Lond. Math. Soc. 54 (2022), 1705-1720. N. Bredon, R. Kellerhals, Hyperbolic Coxeter groups and minimal growth rates in dimensions four and five, Groups Geom. Dyn. 16 (2022), 725-741. R. Kellerhals, Ideal uniform polyhedra in Hn and covolumes of higher dimensional modular groups, Canad. J. Math. 73 (2021), 465-492. R. Kellerhals, M. Belolipetsky and V. Emery, Mini-Workshop: Reflection Groups in Negative Curvature, Oberwolfach Reports, vol. 16, no.2, 2019, pp. 1043-1070. R. Kellerhals, Algebraic aspects of hyperbolic volume, MFO Report 2017. J. Nonaka, R. Kellerhals, The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space, Tokyo J. of Math. 40 (2017), 379-391. R. Kellerhals, On minimal covolume hyperbolic lattices, in: Special Issue "Geometry of Numbers", MDPI Mathematics 2017, vol. 5, 16 pp. R. Guglielmetti, M. Jacquemet, R. Kellerhals, Commensurability of hyperbolic Coxeter groups: theory and computation, RIMS Kôkyûroku Bessatsu B66 (2017), 57-113. R. Guglielmetti, M. Jacquemet, R. Kellerhals, On commensurable hyperbolic Coxeter groups, Geom. Dedicata 183 (2016), 143-167. R. Kellerhals, Commensurability of hyperbolic Coxeter groups, MFO Report No. 38/2014, DOI 10.4171/OWR/2014/38, 29-32. R. Kellerhals, Hyperbolic orbifolds of minimal volume, Comput. Methods Funct. Theory 14 (2014), 465-481. R. Kellerhals, A. Kolpakov, The minimal growth rate of cocompact Coxeter groups in hyperbolic 3-space, Canad. J. Math. 66 (2014), 354-372. R. Kellerhals, Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers, Algebr. Geom. Topol. 13 (2013), 1001-1025. V. Emery, R. Kellerhals, The three smallest compact arithmetic hyperbolic 5-orbifolds, Algebr. Geom. Topol. 13 (2013), 817-829. R. Kellerhals, Scissors congruence, the golden ratio and volumes in hyperbolic 5-space, Discrete and Computational Geometry 47 (2012), 629-658. R. Kellerhals, G. Perren, On the growth of cocompact hyperbolic Coxeter groups, European Journal of Combinatorics 32 (2011), 1299-1316. R. Kellerhals, Ludwig Schläfli - ein genialer Schweizer Mathematiker, Elem. Math. 65 (2010), 165-177. T. Hild, R. Kellerhals, The fcc lattice and the cusped hyperbolic 4-orbifold of minimal volume, J. Lond. Math. Soc. 75 (2007), 677-689. V. Kac, R. Kellerhals, F. Knop, P. Littelmann, D. Panyushev, Special issue in honour of Ernest Borisovich Vinberg, J. Algebra 313 (2007), 1-3. R. Kellerhals, On the structure of hyperbolic manifolds, Israel J. Math. 143 (2004), 361-379. R. Kellerhals, Hyperbolic Coxeter groups and space forms, in: Proceedings Symposium "The Coxeter Legacy: Reflections and Projections", Toronto, 2004, E. Ellers (ed.), Fields Institute. R. Kellerhals, Quaternions and some global properties of hyperbolic 5-manifolds, Canad. J. Math. 55 (2003), 1080-1099. N. Johnson, R. Kellerhals, J. Ratcliffe, S. Tschantz, Commensurability classes of hyperbolic Coxeter simplex reflection groups, Linear Algebra Appl. 345 (2002), 119-147. R. Kellerhals, Collars in PSL(2,H), Annales Academiae Scientiarum Fennicae 26 (2001), 51-72. R. Kellerhals, T. Zehrt, The Gauss-Bonnet formula for hyperbolic manifolds of finite volume, Geometriae Dedicata 84 (2001), 49-62. R. Kellerhals, Old and New about Hilbert's Third Problem. European women in mathematics (Loccum, 1999), 179-187, Hindawi Publ. Corp., Cairo, 2000. N. Johnson, R. Kellerhals, J. Ratcliffe, S. Tschantz, The size of a hyperbolic Coxeter simplex, Transformation Groups 4 (1999), 329-353. R. Kellerhals, Ball packings in spaces of constant curvature and the simplicial density function, J. reine angew. Math. 494 (1998), 189-203. R. Kellerhals, Volumes of cusped hyperbolic manifolds, Topology 37 (1998), 719-734. R. Kellerhals, Nichteuklidische Geometrie und Volumina hyperbolischer Polyeder, Math. Semesterber. 43 (1996), 155-168. R. Kellerhals, Der Mathematiker Ludwig Schläfli (15.01.1814 - 20.03.1895), DMV-Mitteilungen 4 (1996), 35-43. R. Kellerhals, Regular simplices and lower volume bounds for hyperbolic n-manifolds, Annals of Global Analysis and Geometry 13 (1995), 377-392. R. Kellerhals, Shape and size through hyperbolic eyes, The Mathematical Intelligencer 17 (2) (1995), 21-30. R. Kellerhals, Volumes in hyperbolic 5-space, Geom. Funct. Anal. 5 (1995), 640-667. R. Kellerhals, Volumina von hyperbolischen Raumformen, Habilitationsschrift, Universität Bonn, April 1995, Preprint MPI 95-110, 100 pp. R. Kellerhals, On volumes of non-Euclidean polytopes, in: "Polytopes: Abstract, Convex and Computational", 231-239, T. Bisztriczky et al. (eds.), Proceedings NATO ASI 440, Kluwer, Dordrecht, 1994. R. Kellerhals, On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm, Comm. Math. Helv. 67 (1992), 648-663. R. Kellerhals, The dilogarithm and volumes of hyperbolic polytopes, in: "Structural properties of Polylogarithms", Leonard Lewin (ed.), AMS Mathematical Surveys and Monographs, vol. 37 (1991), 301-336. R. Kellerhals, On Schläfli's reduction formula, Math. Z. 206 (1991), 193-210. R. Kellerhals, On the volume of hyperbolic polyhedra, Math. Ann. 285 (1989), 541-569. R. Kellerhals, Über den Inhalt hyperbolischer Polyeder in den Dimensionen drei und vier, Dissertation, Universität Basel 1988, 78 pp. Theses and related publications of my former students N. Bredon, On the existence and growth properties of hyperbolic Coxeter groups, Ph.D. thesis no. 8046, Université de Fribourg 2024. N. Bredon, T. Yukita, Coxeter systems with 2-dimensional Davis complexes, growth rates and Perron numbers, Algebr. Geom. Topol. 24 (2024), 1787-1808. N. Bredon, Hyperbolic Coxeter groups of minimal growth rates in higher dimensions, Canad. Math. Bull. 66 (2023), 232-242. S. T. Drewitz, New contributions to groups of hyperbolic isometries, Ph.D. thesis no. 7817, Université de Fribourg 2021. E. Dotti, On the commensurability of hyperbolic Coxeter groups, Manuscripta Math. 173 (2024), 203-222. E. Dotti, Groups of hyperbolic isometries and their commensurability, Ph.D. thesis no. 2213, Université de Fribourg 2020. E. Dotti, S. T. Drewitz, On right-angled polygons in hyperbolic space, Geom. Dedicata 200 (2019), 45-59. R. Guglielmetti, Hyperbolic isometries in (in-)finite dimensions and discrete reflection groups: theory and computations, Ph.D. thesis no. 2008, Université de Fribourg 2017. M. Jacquemet, On hyperbolic Coxeter n-cubes, European J. Combin. 59 (2017), 192-203. R. Guglielmetti, M. Jacquemet, Polyhedra and commensurability, Snapshot of modern mathematics form Oberwolfach, vol. 9 / 2016, 14pp. R. Guglielmetti, CoxIter - Computing invariants of hyperbolic Coxeter groups, LMS J. Comput. Math. 18 (2015), 754-773. J. Granier, Groupes discrets en géométrie hyperbolique - Aspects effectifs, 'Co-tutelle de thèse' with the University Grenoble Alpes (France), Ph.D. thesis no. 1944, Université de Fribourg 2015. M. Jacquemet, New contributions to hyperbolic polyhedra, reflection groups, and their commensurability, Ph.D. thesis no. 1929, Université de Fribourg 2015. M. Jacquemet, The inradius of a hyperbolic truncated n-simplex, Discrete and Computational Geometry 51 (2014), 997-1016. Y. Umemoto, Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers, Algebraic & Geometric Topolology 14 (2014), 2721-2746. A. Kolpakov, Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers, European J. Comb. 33 (2012), 1709-1724. A. Kolpakov, On the optimality of the ideal right-angled 24-cell, Algebraic & Geometric Topology 12 (2012), 1941-1960. A. Kolpakov, On extremal properties of hyperbolic Coxeter polytopes and their reflection groups, Ph.D. thesis no. 1766, Université de Fribourg 2012. G. Perren, Growth of cocompact hyperbolic Coxeter groups and their rate, Ph.D. thesis no. 1656, Université de Fribourg 2009. R. Kellerhals, G. Perren, On the growth of cocompact hyperbolic Coxeter groups, European Journal of Combinatorics 32 (2011), 1299-1316. V. Emery, Du volume des quotients arithmétiques de l'espace hyperbolique, Ph.D. thesis no. 1648, Université de Fribourg 2009. M. Belolipetsky, V. Emery, On volumes of arithmetic quotients of PO(n,1), n odd, Preprint submitted 2010, arXiv:1001.4670. T. Hild, The cusped hyperbolic orbifolds of minimal volume in dimensions less than ten, J. Algebra 313 (2007), 208-222. T. Hild, Cusped hyperbolic orbifolds of minimal volume in dimensions less than 11, Ph.D. thesis no. 1567, Université de Fribourg 2007. T. Zehrt, The covolume of discrete subgroups of Iso(H^{2m}), Discrete Math. 309 (2009), 2284-2291. T. Zehrt, Schläfli numbers and reduction formula, European J. Combin. 29 (2008), 601-616. A. Felikson, P. Tumarkin, T. Zehrt, On hyperbolic Coxeter n-polytopes with n+2 facets, Adv. Geom. 7 (2007), 177-189. T. Zehrt, Polytopal complexes in spaces of constant curvature, Ph.D. thesis, Universität Basel 2003.