三维子芬斯勒海森堡群中 $(X,Y)$-Lipschitz 曲面的伯恩斯坦问题
微分几何
2022-11-15 v3 度量几何
摘要
我们证明，在具有子芬斯勒结构的海森堡群 中，一个完备、有向、连通且稳定的 -Lipschitz 曲面必为垂直平面。特别地，该结果对欧氏 Lipschitz 函数的整体内蕴图像成立。
引用
@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}
}
备注
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