On self-circumferences in Minkowski planes

Mostafa Ghandehari ^[1] ; Horst Martini
1. [1] University of Texas at Arlington
  
  University of Texas at Arlington
  
  Estados Unidos
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 34, Nº 1, 2019, págs. 19-28
Idioma: inglés
DOI: 10.17398/2605-5686.34.1.19
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Resumen
- This paper contains results on self-circumferences of convex ﬁgures in the frameworks of norms and (more general) also of gauges. Let δ(n) denote the self-circumference of a regular polygon with n sides in a normed plane. We will show that δ(n) is monotonically increasing from 6 to 2π if n is twice an odd number, and monotonically decreasing from 8 to 2π if n is twice an even number. Calculations of self-circumferences for the case that n is odd as well as inequalities for the self-circumference of some irregular polygons are also given. In addition, properties of the mixed area of a plane convex body and its polar dual are used to discuss the self-circumference of convex curves.