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Combinatorica

, Volume 37, Issue 1, pp 99–125 | Cite as

On the perimeter of k pairwise disjoint convex bodies contained in a convex set in the plane

  • Rom Pinchasi
Original Paper
  • 65 Downloads

Abstract

We prove the following isoperimetric inequality in R2, conjectured by Glazyrin and Morić. Given a convex body S and k pairwise disjoint convex bodies C 1,...,C k that are contained in S, then Σ i=1 k Per(C i)≤Per(S)+2(k—1)Diam(S). Here Per(.) denotes the perimeter of a set and Diam(.) is the diameter of a set.

Mathematics Subject Classification (2000)

52A10 52A38 

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References

  1. [1]
    A. Glazyrin and F. Morić: Upper bounds for the perimeter of plane convex bodies, Acta Math. Hungar. 142 (2014), 366–383.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    G. B. Price: On the completeness of a certain metric space with an application to Blaschke’s selection theorem, Bull. Amer. Math. Soc. 46 (1940), 278–280.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mathematics Department Technion—Israel Institute of TechnologyHaifaIsrael

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