Optimizing geometric measures for fixed minimal annulus and inradius

  • María A. Hernández Cifre

    Universidad de Murcia, Spain
  • Pedro J. Herrero Piñeyro

    Universidad de Murcia, Spain

Abstract

In this paper we relate the minimal annulus of a planar convex body KK with its inradius, obtaining all the upper and lower bounds, in terms of these quantities, for the classic geometric measures associated with the set: area, perimeter, diameter, minimal width and circumradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets.

Cite this article

María A. Hernández Cifre, Pedro J. Herrero Piñeyro, Optimizing geometric measures for fixed minimal annulus and inradius. Rev. Mat. Iberoam. 23 (2007), no. 3, pp. 953–971

DOI 10.4171/RMI/520