Coverings by convex bodies and inscribed balls

2003/12/05 by Vladimir Kadets, Kadets, Vladimir
Engineering · Mathematics · #46C05 #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #Structural Analysis and Optimization #math.FA #msc:46C05

paper · pdf · doi:10.48550/arxiv.math/0312133

6 pages

arxiv created 2003/12/05 · openalex publication_date 2003/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a Hilbert space. For a closed convex body A denote by r(A) the supremum of radiuses of balls, contained in A. We prove, that ∑_n=1^∞ r(A_n) ≥ r(A) for every covering of a convex closed body A ⊂ H by a sequence of convex closed bodies A_n, n ∈ \N. It looks like this fact is new even for triangles in a 2-dimensional space.

Citations

• The plank problem for symmetric bodies

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