CMC spheres in the Heisenberg group

Abstract

We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group $H^1$. These spheres are conjectured to be the isoperimetric sets of $H^1$. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit.

References in corpus (1)

• Quantitative isoperimetric inequalities in H^n

Cited by in corpus (1)

• The isoperimetric problem for regular and crystalline norms in ${\mathbb{H}}^1$