For a strictly convex smooth convex body phi, the intersection of n contributing translates with nonempty interior has exactly n boundary singularities.
On convex bodies of constant width
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abstract
We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in $\mathbb R^n$ is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open.
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math.GT 1years
2022 1verdicts
UNVERDICTED 1representative citing papers
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The Number of Singularities in the Intersections of Convex Planar Translates
For a strictly convex smooth convex body phi, the intersection of n contributing translates with nonempty interior has exactly n boundary singularities.