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PreprintarXiv licencearXiv

Catenoid-sharp index-topology estimates for minimal hypersurfaces

  • Junzhang Li
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Abstract

We show that for an embedded two-sided minimal hypersurface in ℝN, there is a lower bound for the index in terms of the first Betti number and the number of ends, using ideas from the recent work of Chodosh--Gianocca. This estimate is sharp for the higher-dimensional catenoid. We also obtain a Spin(7) analogue of Theorem 10.1 of Chodosh--Gianocca: a complete two-sided minimal immersion M7→ℝ8 of index one and finite total curvature is a higher-dimensional catenoid.

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Cite

BibTeXRIS
BibTeX
@misc{li2026catenoidsharp,
  title = {{Catenoid-sharp index-topology estimates for minimal hypersurfaces}},
  author = {Junzhang Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03424},
  eprint = {2609.03424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03424},
}
RIS
TY  - UNPB
TI  - Catenoid-sharp index-topology estimates for minimal hypersurfaces
AU  - Junzhang Li
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03424
UR  - https://arxiv.org/abs/2609.03424
AB  - We show that for an embedded two-sided minimal hypersurface in ℝ^N, there is a lower bound for the index in terms of the first Betti number and the number of ends, using ideas from the recent work of Chodosh--Gianocca. This estimate is sharp for the higher-dimensional catenoid. We also obtain a Spin(7) analogue of Theorem 10.1 of Chodosh--Gianocca: a complete two-sided minimal immersion M^7→ℝ^8 of index one and finite total curvature is a higher-dimensional catenoid.
ER  -