Artículo
On the isodiametric and isominwidth inequalities for planar bisections
Autor/es | Cañete Martín, Antonio Jesús
González Merino, Bernardo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2021 |
Fecha de depósito | 2022-06-23 |
Publicado en |
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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 ... 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. |
Agencias financiadoras | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Junta de Andalucía Fundación Séneca |
Identificador del proyecto | MTM2017-84851-C2-1-P
FQM-325 19901/GERM/15 PGC2018-094215-B-I00 |
Cita | Cañete Martín, A.J. y González Merino, B. (2021). On the isodiametric and isominwidth inequalities for planar bisections. Revista Matemática Iberoamericana, 37 (4), 1247-1275. |
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