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- W4287394930 abstract "The Blaschke-Leichtweiss theorem (Abh. Math. Sem. Univ. Hamburg 75: 257-284, 2005) states that the smallest area convex domain of constant width $w$ in the $2$-dimensional spherical space ${mathbb S}^2$ is the spherical Reuleaux triangle for all $0<wleqfrac{pi}{2}$. In this paper we extend this result to the family of wide $r$-disk domains of ${mathbb S}^2$, where $0<rleqfrac{pi}{2}$. Here a wide $r$-disk domain is an intersection of spherical disks of radius $r$ with centers contained in their intersection. This gives a new and elementary proof of the Blaschke-Leichtweiss theorem. Furthermore, we investigate the higher dimensional analogue of wide $r$-disk domains called wide $r$-ball bodies. In particular, we determine their minimum spherical width (resp., inradius) in the spherical $d$-space ${mathbb S}^d$ for all $dgeq 2$. Also, it is shown that any minimum volume wide $r$-ball body is of constant width $r$ in ${mathbb S}^d$, $dgeq 2$." @default.
- W4287394930 created "2022-07-25" @default.
- W4287394930 creator A5073258078 @default.
- W4287394930 date "2021-01-02" @default.
- W4287394930 modified "2023-09-24" @default.
- W4287394930 title "On a strengthening of the Blaschke-Leichtweiss theorem" @default.
- W4287394930 doi "https://doi.org/10.48550/arxiv.2101.00538" @default.
- W4287394930 hasPublicationYear "2021" @default.
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