R. Monti

Fuglede's theorem in the Heisenberg group

We prove a Fuglede-type quantitative isoperimetric inequality for the Pansu sphere, the conjectured isoperimetric set in the sub-Riemannian Heisenberg group $\mathbb{H}^1$. We show that, among suitable volume-preserving normal perturbations of the Pansu sphere that are small in a weighted $C^2$-norm, the difference bet...