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- W1984154489 abstract "For every hemisphere K supporting a convex body C on the sphere S d we define the width of C determined by K. We show that it is a continuous function of the position of K. We prove that the diameter of every convex body $${C subset S^d}$$ equals the maximum of the widths of C provided the diameter of C is at most $${frac{pi}{2}}$$ . In a natural way, we define spherical bodies of constant width. We also consider the thickness Δ(C) of C, i.e., the minimum width of C. A convex body $${R subset S^d}$$ is said to be reduced if Δ(Z) < Δ(R) for every convex body Z properly contained in R. For instance, bodies of constant width on S d and regular spherical odd-gons of thickness at most $${frac{pi}{2}}$$ on S 2 are reduced. We prove that every reduced smooth spherical convex body is of constant width." @default.
- W1984154489 created "2016-06-24" @default.
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- W1984154489 date "2013-12-06" @default.
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- W1984154489 title "Width of spherical convex bodies" @default.
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- W1984154489 doi "https://doi.org/10.1007/s00010-013-0237-3" @default.
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