The inverse Kakeya problem

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We prove that the largest convex shape that can be placed inside a given convex shape Q subset of R-d in any desired orientation is the largest inscribed ball of Q. The statement is true both when "largest" means "largest volume" and when it means "largest surface area". The ball is the unique solution, except when maximizing the perimeter in the two-dimensional case.
Publisher
SPRINGER
Issue Date
2022-03
Language
English
Article Type
Article
Citation

PERIODICA MATHEMATICA HUNGARICA, v.84, no.1, pp.70 - 75

ISSN
0031-5303
DOI
10.1007/s10998-021-00392-z
URI
http://hdl.handle.net/10203/292399
Appears in Collection
CS-Journal Papers(저널논문)
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