On the isodiametric and isominwidth inequalities for planar bisections
- Antonio Cañete 1
- Bernardo González Merino 2
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1
Universidad de Sevilla
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2
Universidad de Murcia
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ISSN: 0213-2230
Datum der Publikation: 2021
Ausgabe: 37
Nummer: 4
Seiten: 1247-1275
Art: Artikel
Andere Publikationen in: Revista matemática iberoamericana
Zusammenfassung
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.