Is a complete, reduced set necessarily of constant width?-Reference-Cited by-同舟云学术

Is a complete, reduced set necessarily of constant width?

Published:2019-01-01 Issue:1 Volume:19 Page:31-40
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Brandenberg René¹,Merino Bernardo González¹,Jahn Thomas²,Martini Horst²

Affiliation:

1. Zentrum Mathematik, Technische Universität München , Boltzmannstr. 3, 85747 Garching bei München , Germany

2. Fakultät für Mathematik, Technische Universität Chemnitz , 09107 Chemnitz , Germany

Abstract

Abstract Is it true that a convex body K being complete and reduced with respect to some gauge body C is necessarily of constant width, i.e. does it satisfy K − K = ρ(C − C) for some ρ > 0? We prove this implication for several cases including the following: if K is a simplex or if K contains a smooth extreme point, then the implication holds. Moreover, we derive several new results on perfect norms.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2017-0058/pdf

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