## 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

[BibTeX]

Published Paper

Inserted: 7 sep 2010
Last Updated: 25 jul 2017

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 $\mathbb H^1$.