Data evento: 
Giovedì, 17 Luglio, 2014 - 10:30
University of Sussex

Title: The rigidity problem for symmetrization inequalities

GIOVEDI 17 luglio 2014 ore 10,30
AULA dei Seminari Sez. di Fisica
Dipartimento SBAI


Steiner symmetrization is a very useful tool
in the study of isoperimetric inequality.
This is also due to the fact that
the perimeter of a set is less or equal
than the perimeter of its Steiner symmetral.
In the same way, in the Gaussian setting,
it is well known that Ehrhard symmetrization
does not increase the Gaussian perimeter.
We will show characterization results
for equality cases in both Steiner and Ehrhard perimeter inequalities.
We will also characterize rigidity of equality cases.
By rigidity, we mean the situation when all equality cases
are trivially obtained by a translation of the Steiner symmetral
(or, in the Gaussian setting, by a reflection of the Ehrhard symmetral).
We will achieve this through the introduction of a suitable
measure-theoretic notion of connectedness, 
and through a fine analysis of the barycenter function
for a special class of sets.
These results are obtained in collaboration with
Maria Colombo, Guido De Philippis,
and Francesco Maggi.
Per informazioni chiedere a Virginia De Cicco