The Bernstein problem for $(X,Y)$-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups
Differential Geometry
2022-11-15 v3 Metric Geometry
Abstract
We prove that in the Heisenberg group with a sub-Finsler structure, an -Lipschitz surface which is complete, oriented, connected and stable must be a vertical plane. In particular, the result holds for entire intrinsic graphs of Euclidean Lipschitz functions.
Keywords
Cite
@article{arxiv.2105.02179,
title = {The Bernstein problem for $(X,Y)$-Lipschitz surfaces in three-dimensional sub-Finsler Heisenberg groups},
author = {Gianmarco Giovannardi and Manuel Ritoré},
journal= {arXiv preprint arXiv:2105.02179},
year = {2022}
}
Comments
In the third version of the manuscript we consider the Bernstein problem for $(X,Y)$-Lipschitz surfaces that are locally intrinsic graphs of Euclidean Lipschitz functions, see Definition 2.2 and Theorem 2.3. We also add Lemma 3.1, Lemma 3.2 and Lemma 5.1 to deal with the low-regularity of $(X,Y)$-Lipschitz surfaces in the first and second variation formulas