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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
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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

Information

Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982, pp. 194 - 201
Copyright
Copyright © University College London 1982

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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