论文标题
恒定曲率空间和Reuleaux三角形的极端区域的恒定宽度体
Convex bodies of constant width in spaces of constant curvature and the extremal area of Reuleaux triangles
论文作者
论文摘要
在欧几里得飞机上扩展了Blaschke和Lebesgue的经典结果，最近在球形和双曲线病例中也证明了Reuleaux Triangles在恒定宽度$ D $ D $的凸形域之间的区域最小。我们证明，在恒定曲率的三种表面中，每种类型的表面中的每一种都证明了该语句的最佳稳定性版本。此外，我们总结了恒定曲率空间中恒定宽度的凸体的基本特性，并在荷兰的双曲线情况下提供了表征。
Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have the minimal area among convex domains of constant width $D$. We prove an essentially optimal stability version of this statement in each of the three types of surfaces of constant curvature. In addition, we summarize the fundamental properties of convex bodies of constant width in spaces of constant curvature, and provide a characterization in the hyperbolic case in terms of horospheres.
