文章基本信息

标题：On self-circumferences in Minkowski planes
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作者：M. GHANDEHARI ; H. MARTINI
期刊名称：Extracta Mathematicae
印刷版ISSN：0213-8743
出版年度：2019
卷号：34
期号：1
页码：19-28
DOI：10.17398/2605-5686.34.1.19
出版社：Universidad de Extremadura
摘要：This paper contains results on self-circumferences of convex gures in the frameworksof norms and (more general) also of gauges. Let (n) denote the self-circumference of a regularpolygon with n sides in a normed plane. We will show that (n) is monotonically increasing from 6to 2 if n is twice an odd number, and monotonically decreasing from 8 to 2 if n is twice an evennumber. Calculations of self-circumferences for the case that n is odd as well as inequalities for theself-circumference of some irregular polygons are also given. In addition, properties of the mixedarea of a plane convex body and its polar dual are used to discuss the self-circumference of convexcurves.
关键词：Gauge; Minkowski geometry; normed plane; polygonal gauges; Radon curve; self-;circumference; self-perimeter.