Artículo
Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter
Autor/es | Cañete Martín, Antonio Jesús
Schnell, Uwe Segura Gomis, Salvador |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2016 |
Fecha de depósito | 2019-10-23 |
Publicado en |
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Resumen | In this work we study subdivisions of k-rotationally symmetric
planar convex bodies that minimize the maximum relative diameter
functional. For some particular subdivisions called k-partitions, consisting
of k curves ... In this work we study subdivisions of k-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called k-partitions, consisting of k curves meeting in an interior vertex, we prove that the so-called standard k-partition (given by k equiangular inradius segments) is minimizing for any k 2 N, k > 3. For general subdivisions, we show that the previous result only holds for k 6 6. We also study the optimal set for this problem, obtaining that for each k 2 N, k > 3, it consists of the intersection of the unit circle with the corresponding regular k-gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of k, and conjecture the optimal k-subdivision in this case. |
Identificador del proyecto | MTM2010-21206-C02-01
MTM2013-48371-C2-1-P FQM-325 P09-FQM-5088 |
Cita | Cañete Martín, A.J., Schnell, U. y Segura Gomis, S. (2016). Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter. Journal of Mathematical Analysis and Applications, 435 (1), 718-734. |
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