In the Heisenberg group 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.

Area-Minimizing Horizontal Graphs with Low Regularity in the Sub-Finsler Heisenberg Group H^1 / Giovannardi, Gianmarco; Pozuelo, Julián; Ritoré, Manuel. - ELETTRONICO. - (2023), pp. 209-226. [10.1007/978-3-031-39916-9_7]

Area-Minimizing Horizontal Graphs with Low Regularity in the Sub-Finsler Heisenberg Group H^1

Giovannardi, Gianmarco;
2023

Abstract

In the Heisenberg group 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.
2023
978-3-031-39915-2
978-3-031-39916-9
New Trends in Geometric Analysis
209
226
Giovannardi, Gianmarco; Pozuelo, Julián; Ritoré, Manuel
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1343291
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