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PreprintarXiv licencearXiv

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 ℝn+1 of topological type S1× M for any λ≥ 0, where M⊂𝕊n 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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Cite

BibTeXRIS
BibTeX
@misc{junqi2026construction,
  title = {{Construction of compact embedded $λ$-hypersurfaces via isoparametric hypersurfaces}},
  author = {Lai Junqi and Wei Guoxin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23499},
  eprint = {2609.23499},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23499},
}
RIS
TY  - UNPB
TI  - Construction of compact embedded λ-hypersurfaces via isoparametric hypersurfaces
AU  - Lai Junqi
AU  - Wei Guoxin
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23499
UR  - https://arxiv.org/abs/2609.23499
AB  - We construct closed embedded λ-hypersurfaces in ℝ^n+1 of topological type S^1× M for any λ≥ 0, where M⊂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.
ER  -