AI 中文总结
该研究在任意黎曼流形中建立一般平均曲率泛函的一阶和二阶变分公式，通过黎曼近似方案在次黎曼海森堡群中得到对应公式，为相关几何研究提供变分工具。
AI 中文摘要
我们在任意黎曼流形的任意变分下建立一般平均曲率泛函的一阶和二阶变分公式，通过黎曼近似方案在次黎曼海森堡群中得到相应公式。
英文摘要
We establish first and second variation formulas for general mean curvature functionals under arbitrary variations in arbitrary Riemannian manifolds. We obtain corresponding formulas in the sub-Riemannian Heisenberg group through a Riemannian approximation scheme.
CommentsThe material in this article previously appeared in Appendices A and B of arXiv:2605.29912v1, of which the present author is a coauthor. These appendices will be removed from a subsequent version of arXiv:2605.29912, which will instead refer to the present article
