发表机构
South China Normal University（华南师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了任意非负λ下拓扑为S^1×M的闭嵌入λ-超曲面，其中M为等参超曲面，推广了先前结果并补全了Riedler构造的缺失情形。
AI 中文摘要
我们构造了${\mathbb{R}^{n+1}}$中拓扑类型为${S^1\times M}$的闭嵌入${\lambda}$-超曲面，其中${\lambda \ge 0}$，且${M\subset\mathbb{S}^n}$是主曲率重数相等的等参超曲面。这推广了Angenent、McGrath和Riedler（当${\lambda = 0}$时）以及Cheng-Wei和Ross（当${\lambda > 0}$时）的先前结果，特别是补全了Riedler构造中缺失的情形。
英文摘要
We construct closed embedded $λ$-hypersurfaces in ${\mathbb{R}^{n+1}}$ of topological type ${S^1\times M}$ for any ${λ\ge 0}$, where ${M\subset\mathbb{S}^n}$ is an isoparametric hypersurface with equal principal curvature multiplicities. This extends previous results of Angenent, McGrath, and Riedler (for ${λ= 0}$) as well as Cheng-Wei and Ross (for ${λ> 0}$), and in particular completes the missing case of Riedler's construction.
Comments17 pages, Comments Welcome!
