论文标题
Lipschitz边界的规律性具有处方的子纹式均值曲率，在Heisenberg Group $ \ mathbb {h}^1 $
Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group $\mathbb{H}^1$
论文作者
论文摘要
For a strictly convex set $K\subset \mathbb{R}^2$ of class $C^2$ we consider its associated sub-Finsler $K$-perimeter $|\partial E|_K$ in $\mathbb{H}^1$ and the prescribed mean curvature functional $|\partial E|_K-\int_E f$ associated to a function $f$.考虑到这种功能的关键设置，具有欧几里得lipschitz和固有的常规边界，我们证明它们的特征曲线是$ c^2 $的类别，并且这种规律性是最佳的。当$ e $的边界是$ c^1 $的$ e $的边界时，结果尤其成立。
For a strictly convex set $K\subset \mathbb{R}^2$ of class $C^2$ we consider its associated sub-Finsler $K$-perimeter $|\partial E|_K$ in $\mathbb{H}^1$ and the prescribed mean curvature functional $|\partial E|_K-\int_E f$ associated to a function $f$. Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class $C^2$ and that this regularity is optimal. The result holds in particular when the boundary of $E$ is of class $C^1$.
