On the isodiametric and isominwidth inequalities for planar bisections

  1. Antonio Cañete 1
  2. Bernardo González Merino 2
  1. 1 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  2. 2 Universidad de Murcia
    info

    Universidad de Murcia

    Murcia, España

    ROR https://ror.org/03p3aeb86

Revista:
Revista matemática iberoamericana

ISSN: 0213-2230

Año de publicación: 2021

Volumen: 37

Número: 4

Páginas: 1247-1275

Tipo: Artículo

DOI: 10.4171/RMI/1225 DIALNET GOOGLE SCHOLAR

Otras publicaciones en: Revista matemática iberoamericana

Resumen

For a given planar convex body K, a bisection of K is a decomposition of K into two closed sets A,B so that A∩B is an injective continuous curve connecting exactly two boundary points of K. Consider a bisection of K 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.

Fuente de los datos: Dialnet