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A bound for the perimeter of inner parallel bodies
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-0057-8211
2016 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 271, no 3, 610-619 p.Article in journal (Refereed) Published
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Abstract [en]

We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body Ω. The bound depends only on the perimeter and inradius r of the original body and states that. |∂Ωt|≥(1-tr)+n-1|∂Ω|. In particular the bound is independent of any regularity properties of ∂Ω. As a by-product of the proof we establish precise conditions for equality. The proof, which is straightforward, is based on the construction of an extremal set for a certain optimization problem and the use of basic properties of mixed volumes.

Place, publisher, year, edition, pages
Academic Press, 2016. Vol. 271, no 3, 610-619 p.
Keyword [en]
Convex geometry, Inner parallel sets, Perimeter, Primary, Secondary
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-186837DOI: 10.1016/j.jfa.2016.02.022ISI: 000378013400006OAI: oai:DiVA.org:kth-186837DiVA: diva2:931635
Funder
Swedish Research Council, 2012-3864
Note

QC 20160530

Available from: 2016-05-30 Created: 2016-05-13 Last updated: 2016-07-15Bibliographically approved

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