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arXiv · 2204.03474

Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $\mathbb{H}^1$

Gianmarco Giovannardi·Julián Pozuelo·Manuel Ritoré
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Abstract

In the Heisenberg group $\mathbb{H}^1$, 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.

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Gianmarco Giovannardi, Julián Pozuelo, Manuel Ritoré. 2022-04-07. Area-minimizing horizontal graphs with low-regularity in the sub-Finsler Heisenberg group $\mathbb{H}^1$. https://arxiv.org/abs/2204.03474

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