Calculus of Variations and Geometric Measure Theory

The sharp quantitative estimate for the isoperiometric inequality

Aldo Pratelli (University of Pisa)

created by magnani on 21 Nov 2005
modified on 01 Dec 2005

24 nov 2005


Dear All,

next Thursday, 24 November, at 17:30 in ``Sala dei Seminari'' of the Department of Mathematics

Aldo Pratelli, from Pavia University will present

``The sharp quantitative estimate for the isoperiometric inequality''

The abstract follows.

The classical isoperimetric inequality states that, given a set E in Rn with the same volume of the unit ball B, the perimeter P(E) of E is greater than the perimeter P(B) of B. Moreover, if the isoperimetric deficit D(E)=P(E)-P(B) equals 0, than E coincides with (a translation of) B. A quantitative version of the isoperimetric inequality consists in showing that L(E)<D(E)p, where the Fraenkel asymmetry L(E) of E is defined as the volume of the symmetric difference between E and a suitable translation of B (the translation minimizing L(E)!). We will prove the above inequality with p=12, showing also that this is sharp; this result gives a positive answer to a to a conjecture by Hall (given also, in a weaker version, by Bonnesen).