## Seminario

Data evento:

Thursday, July 17, 2014 - 10:30

FILIPPO CAGNETTI

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

Abstract:

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.

Abstract:

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