On the isodiametric and isominwidth inequalities for planar bisections.
A Canete, B González Merino - Revista Mathematica Iberoamericana, 2021 - ems.press
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 …
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 …
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