ON ORTHOGONAL CHORDS IN NORMED PLANES

被引：3

作者：

Alonso, Javier ^{[1
]}

Martini, Horst ^{[2
]}

Mustafaev, Zokhrab ^{[3
]}

机构：

[1] Univ Extremadura, Dept Math, Badajoz 06006, Spain

[2] Univ Technol Chemnitz, Fac Math, D-09107 Chemnitz, Germany

[3] Univ Houston Clear Lake City, Dept Math, Houston, TX 77058 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2011年 / 41卷 / 01期

关键词：

Birkhoff orthogonality; convex figure; constant width; isosceles orthogonality; maximal chord; normed plane;

D O I：

10.1216/RMJ-2011-41-1-23

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that a convex plate of diameter I in the Euclidean plane is of constant width 1 if and only if any two perpendicular intersecting chords have total length at least 1. We show that, in general, this result cannot be extended to normed (or Minkowski) planes when the type of orthogonality is defined in the sense of Birkhoff. Inspired by this, we present also further results on intersecting chords in normed planes that are orthogonal in the sense of Birkhoff and in the sense of James.

引用

页码：23 / 35

页数：13

共 50 条

[21] Isoperimetric Inequalities in Normed Planes
dos Santos, Rafael S.
Craizer, Marcos
JOURNAL OF CONVEX ANALYSIS, 2022, 29 (02) : 321 - 331
[22] Reduced bodies in normed planes
Fabinska, Ewa
Lassak, Marek
ISRAEL JOURNAL OF MATHEMATICS, 2007, 161 (01) : 75 - 87
[23] On regular figures in normed planes
Peukert C.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2011, 52 (2): : 463 - 477
[24] CONCURRENT AND PARALLEL CHORDS OF SPHERES IN NORMED LINEAR SPACES
Martini, Horst
Wu, Senlin
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2010, 47 (04) : 505 - 512
[25] The inverse problem on Roulettes in normed planes
Balestro, Vitor
Horvath, Akos G.
Martini, Horst
ANALYSIS AND MATHEMATICAL PHYSICS, 2019, 9 (04) : 2413 - 2434
[26] The local Steiner problem in normed planes
Swanepoel, KJ
NETWORKS, 2000, 36 (02) : 104 - 113
[27] On the circular hull property in normed planes
H. Martini
M. Spirova
Acta Mathematica Hungarica, 2009, 125 : 275 - 285
[28] The inverse problem on Roulettes in normed planes
Vitor Balestro
Ákos G. Horváth
Horst Martini
Analysis and Mathematical Physics, 2019, 9 : 2413 - 2434
[29] Maximum Spanning Trees in Normed Planes
Alonso, Javier
Martin, Pedro
GRAPHS AND COMBINATORICS, 2021, 37 (04) : 1385 - 1403
[30] A new type of orthogonality for normed planes
Horst Martini
Margarita Spirova
Czechoslovak Mathematical Journal, 2010, 60 : 339 - 349

← 1 2 3 4 5 →