Research Article

Cross-section measures, radii, and Radon curves

Published in: Quaestiones Mathematicae
Volume 46 , issue 9 , 2023 , pages: 1925–1936

DOI: 10.2989/16073606.2022.2112631

Author(s): Horst Martini University of Technology Chemnitz, Germany , Zokhrab Mustafaev University of Houston-Clear Lake, USA

Keywords: 52A20 , 52A21 , 52A40 , Busemann measure , cross-section measures , Holmes-Thompson measure , inner radius , intersection body , isoperimetrix , Minkowski space , outer radius , projection body , Radon curves

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Abstract

The purpose of this paper is to study cross-section measures and their connections to Radon curves in two-dimensional Minkowski spaces. More precisely, we use results on cross-section measures to present, for nomed planes, inner and outer radii of the unit ball with respect to its isoperimetrix. This yields new characterizations of and further results on Radon curves.

« On central automorphisms of finite p-groups of class 2