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

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 k i=1 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.

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References

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Correspondence to Rom Pinchasi.

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This research was supported by ISF grant (grant No. 1357/12)

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Pinchasi, R. On the perimeter of k pairwise disjoint convex bodies contained in a convex set in the plane. Combinatorica 37, 99–125 (2017). https://doi.org/10.1007/s00493-015-3217-5

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Mathematics Subject Classification (2000)

  • 52A10
  • 52A38