4 papers
On the minimizer of the barycentric isoperimetric ratio among connected planar sets
Chiara Gambicchia, Aldo Pratelli, Clara Torres-Latorre
Among connected, planar sets, the ratio between the isoperimetric deficit and the squared barycentric asymmetry is known to be bounded from below by a strictly positive constant (a…
The double spherical cap rearrangement of planar sets
Chiara Gambicchia
This paper is devoted to the proof of an isoperimetric property of the double spherical cap rearrangement of planar sets under the assumption of disconnection of non-trivial spheri…
Barycentric stability of nonlocal perimeters: the convex case
Chiara Gambicchia, Enzo Maria Merlino, Berardo Ruffini +1
In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonl…
The sharp quantitative barycentric isoperimetric inequality for bounded sets
Chiara Gambicchia, Aldo Pratelli
We prove the sharp quantitative isoperimetric inequality in the case of the barycentric asymmetry, for bounded sets. This generalizes the -D case recently proved in~\cite{BCH}.