A generalization of domains of constant width

Recently, Ou and Pan introduced the higher order width functions of convex domains, and posed a generalization of the Blaschke–Lebesgue problem: among all convex domains having constant k -order width, which has the least possible area. In this paper, we continue to study convex domains having const...

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Bibliographic Details
Published inBeiträge zur Algebra und Geometrie Vol. 57; no. 1; pp. 259 - 270
Main Author Zhang, Deyan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016
Subjects
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
Equiangular polygon
Perimeter
52A40
Convex domain
Constant width
Higher order width
52A38
Diameter
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Summary:Recently, Ou and Pan introduced the higher order width functions of convex domains, and posed a generalization of the Blaschke–Lebesgue problem: among all convex domains having constant k -order width, which has the least possible area. In this paper, we continue to study convex domains having constant k -order width and obtain some characterizations of this class of sets, which are slightly different from those of constant width convex domains.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-015-0252-8