[CvGmt News] (no subject)

[Valentino Magnani]

~~~~~~~~~~~~~Seminars of the CVGMT research group~~~~~~~~~~~~

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
R^n 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=1/2, 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).