2 papers
math.AP2010
Best constants for the isoperimetric inequality in quantitative form
Marco Cicalese, Gian Paolo Leonardi
We prove existence and regularity of minimizers for a class of functionals defined on Borel sets in . Combining these results with a refinement of the selection principle intr…
math.MG2010
Isodiametric sets in the Heisenberg group
Gian Paolo Leonardi, Severine Rigot, Davide Vittone
In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among a…