Venue
Aula Magna – Dipartimento di Matematica.
Abstract
The convex components of a set (with non-empty interior) are not uniquely determined in general. In this talk, after having recalled some elementary (quantitative) monotonicity properties of the Euclidean perimeter, we study some lower bounds on the minimal number of convex components of an arbitrary set, showing the sharpness of our results with some explicit examples. This is a joint work in collaboration with F. Giannetti.