Trisections of a 3-rotationally symmetric planar convex body minimizing the maximum relative diameter

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Title: Trisections of a 3-rotationally symmetric planar convex body minimizing the maximum relative diameter
Authors: Cañete, Antonio | Miori, Cinzia | Segura Gomis, Salvador
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Fencing problems | 3-rotationally symmetric convex body | Maximum relative diameter
Knowledge Area: Geometría y Topología
Issue Date: 24-Apr-2014
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2014, Accepted Manuscript, Available online 24 April 2014. doi:10.1016/j.jmaa.2014.04.041
Abstract: In this work we study the fencing problem consisting of finding a trisection of a 3-rotationally symmetric planar convex body which minimizes the maximum relative diameter. We prove that an optimal solution is given by the so-called standard trisection. We also determine the optimal set giving the minimum value for this functional and study the corresponding universal lower bound.
Sponsor: The first author is partially supported by MCyT research project MTM2010-21206-C02-01. The second author is partially supported by MINECO (Ministerio de Economía y Competitividad) and FEDER (Fondo Europeo de Desarrollo Regional) project MTM2012-34037 and Fundación Séneca project 04540/GERM/06, Spain. This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology (Regional Plan for Science and Technology 2007-2010).
URI: http://hdl.handle.net/10045/36858
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2014.04.041
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2014.04.041
Appears in Collections:INV - CADAGL - Artículos de Revistas

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