A bound for the perimeter of inner parallel bodies

• Main Author: Larson, Simon
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: Elsevier 2016
• Subjects: Convex geometry; Perimeter; Inner parallel sets; Ari; laptev
• Online Access: https://doi.org/10.1016/j.jfa.2016.02.022

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 |∂Ω_t| ≥ (1−t/r)^(n−1)₊|∂Ω|. In particular the bound is independent of any regularity properties...