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

Rom Pinchasi

doi:10.1007/s00493-015-3217-5

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

Rom Pinchasi

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 C₁,..,C_k that are contained in S, then Σ_i=1 ^kPer(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.

Original language	English
Pages (from-to)	99-125
Number of pages	27
Journal	Combinatorica
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/s00493-015-3217-5
State	Published - 1 Feb 2017

Keywords

52A10
52A38

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-015-3217-5

Cite this

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abstract = "We prove the following isoperimetric inequality in R2, conjectured by Glazyrin and Mori{\'c}. Given a convex body S and k pairwise disjoint convex bodies C1,..,Ck that are contained in S, then Σi=1 kPer(Ci)≤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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AB - We prove the following isoperimetric inequality in R2, conjectured by Glazyrin and Morić. Given a convex body S and k pairwise disjoint convex bodies C1,..,Ck that are contained in S, then Σi=1 kPer(Ci)≤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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KW - 52A38

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DO - 10.1007/s00493-015-3217-5

M3 - مقالة

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JO - Combinatorica

JF - Combinatorica

IS - 1

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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