论文标题
CMC通过Min-Max的最小表面加倍
Cmc Doublings of Minimal Surfaces via Min-Max
论文作者
论文摘要
令$σ^2 \子集m^3 $为索引0或1的最小表面。假设$σ$的邻域可以通过恒定平均曲率（CMC）Hypersurfaces散落。我们使用Min-Max理论和Catenoid估计来构建$ \ VAREPSILON $ -CMC双打$σ$的小$ \ Varepsilon> 0 $。以前，此类CMC双打是为最小的Hypersurfaces构建的$σ^n \ subset m^{n+1} $，使用胶水和Sun使用粘合方法，并使用$ N+1 \ ge 4 $。
Let $Σ^2 \subset M^3$ be a minimal surface of index 0 or 1. Assume that a neighborhood of $Σ$ can be foliated by constant mean curvature (cmc) hypersurfaces. We use min-max theory and the catenoid estimate to construct $\varepsilon$-cmc doublings of $Σ$ for small $\varepsilon > 0$. Such cmc doublings were previously constructed for minimal hypersurfaces $Σ^n \subset M^{n+1}$ with $n+1\ge 4$ by Pacard and Sun using gluing methods.
