The monotonicity of the perimeter of bounded convex sets with respect to the inclusion is well known. In the two dimensional case we give a quantitative version of such a monotonicity. Moreover, in any dimension, we estimate from below the number of convex components of a set.
Convex components of a set and the measure of its boundary
LEONETTI, Francesco
2009-01-01
Abstract
The monotonicity of the perimeter of bounded convex sets with respect to the inclusion is well known. In the two dimensional case we give a quantitative version of such a monotonicity. Moreover, in any dimension, we estimate from below the number of convex components of a set.File in questo prodotto:
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