A bound for the perimeter of inner parallel bodies
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) PublishedText
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.
Convex geometry, Inner parallel sets, Perimeter, Primary, Secondary
IdentifiersURN: urn:nbn:se:kth:diva-186837DOI: 10.1016/j.jfa.2016.02.022ISI: 000378013400006OAI: oai:DiVA.org:kth-186837DiVA: diva2:931635
FunderSwedish Research Council, 2012-3864
QC 201605302016-05-302016-05-132016-07-15Bibliographically approved