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arXiv · 2609.23499

Construction of compact embedded $λ$-hypersurfaces via isoparametric hypersurfaces

Lai Junqi·Wei Guoxin
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Abstract

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.

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Lai Junqi, Wei Guoxin. 2026-09-20. Construction of compact embedded $λ$-hypersurfaces via isoparametric hypersurfaces. https://arxiv.org/abs/2609.23499

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