Stefani: Archimedes, a dinner and a theorem - A divertissement on on the monotonicity of perimeter
Stefani: If $A$ and $B$ are two convex bodies in the Euclidean $n$-dimensional space and $A$ is contained in $B$, then the perimeter of $A$ does not exceed the perimeter of $B$. This monotonicity property of the perimeter dates back to the ancient Greek and Archimedes himself took it as a postulate in his celebrated work on the sphere and the cylinder. A few years ago, a couple of papers by M. Carozza, F. Giannetti, F. Leonetti, and A. Passarelli di Napoli established lower bounds on the difference of the perimeters of A and B in terms of their Hausdorff distance when $n=2$ and $n=3$. In this talk, after a brief introduction on the problem and the known results, I will generalise these lower bounds to any dimension $n$. Time permitting, I will show how this approach can be extended to the case of anisotropic Wulff perimeters. http://cvgmt.sns.it/seminar/637/
When
Tue Apr 24, 2018 12:30pm – 1:30pm Coordinated Universal Time
Where
Aula Riunioni, Dip. di Matematica, Univ. di Pisa (map)
