Quantitative isoperimetric inequalities in H^n

Abstract

In the Heisenberg group H^n, 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.

Cited by in corpus (4)

• The isoperimetric problem for regular and crystalline norms in ${\mathbb{H}}^1$
• Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group ${\mathbb{H}}^1$
• CMC spheres in the Heisenberg group
• A minimal partition problem with trace constraint in the Grushin plane