Calculus of Variations and Geometric Measure Theory

V. Franceschi - G. P. Leonardi - R. Monti

Quantitative isoperimetric inequalities in $\mathbb H ^n$

created by monti on 20 Mar 2015
modified by franceschi on 14 Jul 2016


Published Paper

Inserted: 20 mar 2015
Last Updated: 14 jul 2016

Journal: Calc. Var. Partial Differential Equations
Volume: 54
Number: 3
Pages: 3229-3239
Year: 2015
Doi: 10.1007/s00526-015-0899-x


In the Heisenberg group $\mathbb H^{n}$, $n\geq 1$, we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions. The inequalities are shown for suitably restricted classes of competing sets and the proof relies on the construction of sub-calibrations.