Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T21:19:24.595Z Has data issue: false hasContentIssue false
  • English
  • Français

Slices of L. Fejes Tóth's sausage conjecture

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

U. Betke ,
P. Gritzmann  and
J. M. Wills
U. Betke
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse 3, D-5900 Siegen
P. Gritzmann
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse 3, D-5900 Siegen
J. M. Wills
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse 3, D-5900 Siegen
Get access

Extract

Let be k non-overlapping translates of the unit d-ball Bd in euclidean d-space Ed. Let Ck denote the convex hull of their centres and let Sk be a segment of length 2(k– 1). Furthermore, let Vd denote the d-volume. L. Fejes Tóth conjectured in [1], that, for d ≥ 5,

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 194 - 201
Copyright
Copyright © University College London 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Tóth, L. FejesResearch problem 13. Periodica Math. Hung., 6 (1975).Google Scholar
2.McMullen, P.Non-linear angle-sum relations for polyhedral cones and polytopes. Math. Proc. Camb. Phil. Soc., 78 (1975), 247–261CrossRefGoogle Scholar
3.Kleinschmidt, P. and Pachner, U. and Wills, J. M. On L. Fejes TÓth's sausage conjecture. Discrete Math. To appearGoogle Scholar