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