Discrete & Computational Geometry

, Volume 15, Issue 4, pp 467–479 | Cite as

Central points for sets in ℝn (or: the chocolate ice-cream problem)

  • S. Hoory
  • N. Linial
Article

Abstract

LetA be a subset of the unit ball in ℝn, and let 0≤r≤1 be real. Find a pointx for which the intersection of ther-neighborhood ofx withA has a large measure. Tight bounds on this measure are found.

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References

  1. [C] R. Courant,Differential and Integral Calculus, Vol. II, Blackie, London, 1962, pp. 302–304.Google Scholar
  2. [LPRS] N. Linial, D. Peleg, Yu. Rabinovich, M. Saks, Sphere Packing and Local Majorities in Graphs,Proceedings of the Second Israel Symposium on Theory and Computing Systems, 1993, pp. 141–149.Google Scholar
  3. [T] A. Torchinsky,Real-Variable Methods in Harmonic Analysis, Academic Press, New York, 1986, chapter IV.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • S. Hoory
    • 1
  • N. Linial
    • 1
  1. 1.Institute of Computer ScienceHebrew UniversityJerusalemIsrael

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