naa a22 4500 510736645 CHVBK 20180411083012.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-012-0123-5 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0123-5 On a relative isodiametric inequality for centrally symmetric, compact, convex surfaces [Elektronische Daten] [A. Cerdán, U. Schnell, S. Gomis] We consider the problem of dividing a centrally symmetric, compact, convex surface into two regions in such a way that the intrinsic diameter of both regions is as small as possible. We discuss the best upper bound for the ratio between the area of the smallest region (relative area) and the maximal relative intrinsic diameter. We provide necessary and sufficient conditions for attaining the equality sign. As a consequence from these conditions, there are many surfaces for which the equality sign is never attained. We present a complete study of the special case of the cube surface obtaining the best possible upper bound for this surface. The Managing Editors, 2012 Geometric inequalities nationallicence Convex surfaces nationallicence Central symmetry nationallicence Intrinsic diameter nationallicence Isodiametric inequalities nationallicence Antipodality nationallicence Cerdán A. Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, 03080, Alicante, Spain aut Schnell U. Fachbereich Mathematik/Naturwissenschaften, University of Applied Sciences Zittau/Görlitz, 02763, Zittau, Germany aut Gomis S. Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, 03080, Alicante, Spain aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 277-289 0138-4821 54:1<277 2013 54 13366 https://doi.org/10.1007/s13366-012-0123-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0123-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cerdán A. Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, 03080, Alicante, Spain aut NATIONALLICENCE 700 1- Schnell U. Fachbereich Mathematik/Naturwissenschaften, University of Applied Sciences Zittau/Görlitz, 02763, Zittau, Germany aut NATIONALLICENCE 700 1- Gomis S. Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, 03080, Alicante, Spain aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 277-289 0138-4821 54:1<277 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer