论文标题
具有对称边界的超曲面的对称性
Symmetry of hypersurfaces with symmetric boundary
论文作者
论文摘要
令$ g $为$（n+1）$的紧凑型连接子组。在$ \ mathbb {r}^{n+1} $中，我们获得了内部$ g $ -Smmetry，用于最小值的高空和持续平均曲率（CMC）的高度，这些曲率（CMC）具有$ g $ invariant界限和$ g $ g $ g $ - $ g $ - $ g $ impiniant contact in Bunceles沿线的接触。证明的主要成分是基于无限的谎言群体的行动来建立一个相关的库奇问题，并应用莫里的规律性理论和凯奇·科瓦莱维斯卡亚定理。此外，我们还研究了从$ \ Mathbb {r}^{n+1} $中的恒定高阶平均曲率和helfrich-type Hypersurfaces的超顺序均值曲率和Helfrich-type Hypersurfaces的界面的相同类型的对称性继承。
Let $G$ be a compact connected subgroup of $SO(n+1)$. In $\mathbb{R}^{n+1}$, we gain interior $G$-symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (CMC) which have $G$-invariant boundaries and $G$-invariant contact angles along boundaries. The main ingredients of the proof are to build an associated Cauchy problem based on infinitesimal Lie group actions, and to apply Morrey's regularity theory and the Cauchy-Kovalevskaya Theorem. Moreover, we also investigate the same kind of symmetry inheritance from boundaries for hypersurfaces of constant higher order mean curvature and Helfrich-type hypersurfaces in $\mathbb{R}^{n+1}$.
