Heisenberg 群中最小超曲面的曲率估计
微分几何
2025-05-29 v2
摘要
本文考察了子黎西米尔 Heisenberg 群中的最小超曲面。我们将著名的 Simons 公式和 Kato 不等式推广到亚黎西米尔情形，并将其用于获得稳定型超曲面的积分曲率估计。这些结果导致了蕴含第二 Heisenberg 群中光滑、非特征性超曲面 Bernstein 型刚性定理的结构条件。
引用
@article{arxiv.2409.20359,
title = {Curvature estimates for minimal hypersurfaces in the Heisenberg group},
author = {Gianmarco Giovannardi and Andrea Pinamonti and Simone Verzellesi},
journal= {arXiv preprint arXiv:2409.20359},
year = {2025}
}
备注
With respect to the previous version, we removed one assumption from the proof of the Simons formula and we added several instances to justify some structural properties we introduced