3 papers
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…
math.DG2009
Some isoperimetric problems in planes with density
Antonio Cañete, Michele Miranda, Davide Vittone
We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteris…
math.CA2006
An intrinsic measure for submanifolds in stratified groups
V. Magnani, D. Vittone
For each submanifold of a stratified group, we find a number and a measure only depending on its tangent bundle, the grading and the fixed Riemannian metric. In two step stratified…