Leírás
BME Geometria Szeminárium
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 §2 is the spherical Reuleaux triangle for all 0<w≤π2. In this paper we extend this result to the family of wide r-disk domains of §2, where 0<r≤π2. 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 short proof for 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 §d for all d≥2. Also, it is shown that any minimum volume wide r-ball body is of constant width r in §d, d≥2.