When is a spherical body of constant diameter of constant width?
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DOI: 10.1007/s00010-020-00706-5
Abstract: We prove that a smooth convex body of diameter $$\delta < \frac{\pi }{2}$$ δ < π 2 on the d -dimensional unit sphere $$S^d$$ S d is of constant diameter $$\delta $$ δ if and… read more here.
Keywords: constant diameter; constant width; spherical body; diameter ... See more keywords
Thin sets of constant width
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DOI: 10.1016/j.jmaa.2018.09.053
Abstract: Abstract We prove that every Banach space which admits an unconditional basis can be renormed to contain a constant width set with empty interior, thus guaranteeing, for the first time, existence of such sets in… read more here.
Keywords: thin sets; sets constant; constant width;
Evolving convex surfaces to constant width ones
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DOI: 10.1142/s0129167x17500823
Abstract: Given an n-dimensional convex surface X0 in the Euclidean space ℝn+1, this initial surface can be deformed into a convex surface with constant width by a new evolution model which preserves the convexity of the… read more here.
Keywords: surface; convex; constant width; surfaces constant ... See more keywords