In the setting of the sub-Riemannian Heisenberg group 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 area-minimizing surfaces, i.e., of graphs with the least possible area among those with the same boundary. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of t-graphs in H^1.
Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups
VITTONE, DAVIDE
2014
Abstract
In the setting of the sub-Riemannian Heisenberg group 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 area-minimizing surfaces, i.e., of graphs with the least possible area among those with the same boundary. For minimal graphs we also prove a local boundedness result which is sharp at least in the case of t-graphs in H^1.
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