On the isodiametric and isominwidth inequalities for planar bisections

  • Antonio Cañete

    Universidad de Sevilla, Spain
  • Bernardo González Merino

    Universidad de Murcia, Spain
On the isodiametric and isominwidth inequalities for planar bisections cover
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Abstract

For a given planar convex body , a bisection of is a decomposition of into two closed sets so that is an injective continuous curve connecting exactly two boundary points of . Consider a bisection of minimizing, over all bisections, the maximum diameter (resp., maximum width) of the sets in the decomposition.

In this note, we study some properties of these minimizing bisections and prove inequalities extending the classical isodiametric and isominwidth inequalities. Furthermore, we address the corresponding reverse optimization problems and establish inequalities similar to the reverse isodiametric and reverse isominwidth inequalities.

Cite this article

Antonio Cañete, Bernardo González Merino, On the isodiametric and isominwidth inequalities for planar bisections. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1247–1275

DOI 10.4171/RMI/1225