Calculus of Variations and Geometric Measure Theory

F. Serra Cassano - D. Vittone

Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups

created by vittone on 07 Sep 2010
modified on 25 Jul 2017


Published Paper

Inserted: 7 sep 2010
Last Updated: 25 jul 2017

Journal: Adv. Calc. Var.
Volume: 7
Number: 4
Pages: 409--492
Year: 2014


In the setting of the sub-Riemannian Heisenberg group $\mathbb H^n$, we introduce and study the classes of $t$- and intrinsic graphs of bounded variation. For both notions we prove the existence of non-parametric minimal surfaces, i.e., of graphs which are boundaries of sets minimizing the perimeter measure. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of $t$-graphs in $\mathbb H^1$.

Keywords: minimal surfaces, Heisenberg group, bounded variation, sub-Riemannian geometry