论文标题
完整的球形凸体
Complete Spherical Convex Bodies
论文作者
论文摘要
与$ e^d $中的经典概念类似，一个正直径的子集以下是$ \fracπ{2} $的球体半球$ s^d $的半球称为完整，但前提是增加任何额外点会增加其直径。完整的套件是$ s^d $上的凸面。我们的主要定理说，在$ s^d $上，直径$δ$的完整物体与恒定宽度$δ$相吻合。
Similarly to the classic notion in $E^d$, a subset of a positive diameter below $\fracπ{2}$ of a hemisphere of the sphere $S^d$ is called 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 $δ$ coincide with bodies of constant width $δ$.
