Complete spherical convex bodies

被引：5

作者：

Lassak, Marek ^{[1
]}

机构：

[1] Univ Technol & Life Sci, Al Prof Kaliskiego 7, PL-85796 Bydgoszcz, Poland

来源：

JOURNAL OF GEOMETRY | 2020年 / 111卷 / 02期

关键词：

Sphere; lune; convex body; complete body; constant width; constant diameter;

D O I：

10.1007/s00022-020-00547-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Similarly to the classic notion in Euclidean space, we call a set on the sphere S-d complete, provided adding any extra point increases its diameter. Complete sets are convex bodies on S-d. Our main theorem says that on S-d complete bodies of diameter delta coincide with bodies of constant width delta.

引用

页数：6

共 13 条

[1] Bonnesen T., 1934, Theorie der Konvexen Korper
[2] Chakerian GD., 1983, Convex Bodies of Constant Width. Convexity and its Applications, P49
[3] Eggleston HG., 1958, Cambridge Tracts in Mathematics and Mathematical Physics
[4] Han H., ARXIV190509098V2
[5] On convex constant width point sets
Jessen, B
[J]. MATHEMATISCHE ZEITSCHRIFT, 1929, 29 : 378 - 380
[6] When is a spherical body of constant diameter of constant width?
Lassak, Marek
[J]. AEQUATIONES MATHEMATICAE, 2020, 94 (02) : 393 - 400
[7] Spherical bodies of constant width
Lassak, Marek
Musielak, Micha
[J]. AEQUATIONES MATHEMATICAE, 2018, 92 (04) : 627 - 640
[8] Width of spherical convex bodies
Lassak, Marek
[J]. AEQUATIONES MATHEMATICAE, 2015, 89 (03) : 555 - 567
[9] Lebesgue H., 1921, J. Math. Pures Appl., V4, P67
[10] Martini M, 2019, BODIES CONSTANT WIDT

← 1 2 →