Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $\mathbb{H}^1$
Differential Geometry
2023-05-03 v2
Abstract
In the Heisenberg group , equipped with a left-invariant and not necessarily symmetric norm in the horizontal distribution, we provide examples of entire area-minimizing horizontal graphs which are locally Lipschitz in Euclidean sense. A large number of them fail to have further regularity properties. The examples are obtained by prescribing as singular set a horizontal line or a finite union of horizontal half-lines extending from a given point. We also provide examples of families of area-minimizing cones.
Keywords
Cite
@article{arxiv.2204.03474,
title = {Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $\mathbb{H}^1$},
author = {Gianmarco Giovannardi and Julián Pozuelo and Manuel Ritoré},
journal= {arXiv preprint arXiv:2204.03474},
year = {2023}
}