Skip to main content
Log in

Volumes in hyperbolic 5-space

  • Published:
Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [AVSo]D. V. Alekseevskij, E.B. Vinberg, A.S. Solodovnikov, Geometry of spaces of constant curvature, In “Geometry II, Encyclopaedia of Math. Sciences”, vol. 29, 1993.

  • [B]J. Böhm, Inhaltsmessung im R5 konstanter Krümmung, Arch. Math. 11 (1960), 298–309.

    Google Scholar 

  • [BHe]J. Böhm, E. Hertel, Polyedergeometrie inn-dimensionalen Räumen konstanter Krümmung, Birkhäuser, Basel, 1981.

    Google Scholar 

  • [C]J.-L. Cathelineau, Homologie du groupe linéaire et polylogarithmes [d'après A.B. Goncharov et d'autres], Séminaire Bourbaki, 45ème année, no. 772 (1992–93), 1–23.

    Google Scholar 

  • [Co1]H.S.M. Coxeter, The functions of Schläfli and Lobatschefsky, Quart. J. Math. (Oxford) 6 (1935), 13–29.

    Google Scholar 

  • [Co2]H.S.M. Coxeter, On Schläfli's generalization of Napier's Pentagramma Mirificum, Bull. Calcutta Math. Soc. 28 (1936), 125–144.

    Google Scholar 

  • [Co3]H.S.M. Coxeter, Frieze patterns, Acta Arithmetica, 18 (1971), 297–310.

    Google Scholar 

  • [D]H.E. Debrunner, Dissecting orthoschemes into orthoschemes, Geom. Dedicata 33 (1990), 123–152.

    Google Scholar 

  • [DuS]J.L. Dupont, C.H. Sah, Scissors congruences, II, J. Pure Appl. Algebra 25 (1982), 159–195.

    Google Scholar 

  • [HMu]U. Haagerup, H.J. Munkholm, Simplices of maximal volume in hyperbolic n-space, Acta Math. 147 (1981), 1–12.

    Google Scholar 

  • [IH]H.-C. Im Hof, Napier cycles and hyperbolic Coxeter groups, Bull. Soc. Math. Belgique, Série A, 42 (1990), 523–545.

    Google Scholar 

  • [K1]R. Kellerhals, On the volume of hyperbolic polyhedra, Math. Ann. 285 (1989), 541–569.

    Google Scholar 

  • [K2]R. Kellerhals, The dilogarithm and volumes of hyperbolic polytopes, In “Structural Properties of Polylogarithms” (L. Lewin, ed.), AMS Mathematical Surveys and Monographs 37, 1991.

  • [K3]R. Kellerhals, On volumes of hyperbolic 5-orthoschemes and the trilogarithm, Comment. Math. Helvetici 67 (1992), 648–663.

    Google Scholar 

  • [K4]R. Kellerhals, On volumes of non-Euclidean polytopes, In: “Polytopes: Abstract, Convex and Computational” (T. Bisztriczky et al., eds.), Proceedings NATO ASI 440, Kluwer, Dordrecht, 1994.

    Google Scholar 

  • [L]L. Lewin, Polylogarithms and Associated Functions, North Holland, N.Y., Oxford, 1981.

    Google Scholar 

  • [Lo]N.I. Lobachevskij, Zwei geometrische Abhandlungen, Teubner, Leipzig, 1898.

    Google Scholar 

  • [M]J. Milnor, On polylogarithms, Hurwitz zeta functions, and the Kubert identities, L'Enseignement Mathématique t. 29 (1983), 281–322.

    Google Scholar 

  • [Mü]P. Müller, Über Simplexinhalte in nichteuklidischen Räumen, Dissertation Universität Bonn, 1954.

  • [RT]J.G. Ratcliffe, S.T. Tschantz, Volumes of hyperbolic manifolds, Research Announcement, 1994.

  • [S]C.H. Sah, Scissors congruences, I, Gauss-Bonnet map, Math. Scand. 49 (1981), 181–210.

    Google Scholar 

  • [Sc]L. Schläfli, Theorie der vielfachen Kontinuität, In “Gesammelte Mathematische Abhandlungen” 1, Birkhäuser, Basel, 1950.

    Google Scholar 

  • [V]E.B. Vinberg, Hyperbolic reflection groups, Russ. Math. Surv. 40 (1985), 31–75.

    Google Scholar 

  • [W]H.-C. Wang, Topics in totally discontinuous groups, In “Symmetric Spaces” (W.M. Boothby, G.L. Weiss, eds.), Pure Appl. Math. 8, Marcel Dekker, New York, 1972.

    Google Scholar 

  • [We]G. Wechsung, Functional equations of hyperlogarithms, In “Structural Properties of Polylogarithms” (L. Lewin, ed.), AMS Mathematical Surveys and Monographs 37, 1991.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kellerhals, R. Volumes in hyperbolic 5-space. Geometric and Functional Analysis 5, 640–667 (1995). https://doi.org/10.1007/BF01902056

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01902056

Navigation