Minimum Area of a Set of Constant Width in the Hyperbolic Plane

被引：0
作者：
Paulo Ventura Ara
机构：
[1] Faculdade de Ci do Porto,Centro de Matem
来源：
Geometriae Dedicata | 1997年 / 64卷 / 1期
关键词：
Constant width; Reuleaux triangle; hyperbolic plane.;
D O I：
10.1023/A:1004920201363
中图分类号：
学科分类号：
摘要：
We prove that, in the hyperbolic plane, the Reuleaux triangle has smaller area than any other set of the same constant width.
引用
收藏
页码：41 / 53
页数：12
相关论文
共 5 条
[1]  
Besicovitch A. S.(1963)Minimum area of a set of constant width, in convexity (Seattle 1961) Proceedings of Symposia in Pure Mathematics VII 13-14
[2]  
Dekster B. V.(1992)Width and breadth for convex bodies in Riemannian manifolds Arch. Math 58 190-198
[3]  
Eggleston H. G.(1952)A proof of Blaschke's theorem on the Reuleaux triangle Quart. J. Math 3 296-297
[4]  
Santaló L. A.(1945)Note on convex curves on the hyperbolic plane Bull. Amer.Math. Soc. 51 405-412
[5]  
Wegner B.(1981)Einige Bemerkungen zur Geometrie transnormaler Mannigfaltigkeiten J. Differential Geom. 16 93-100
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