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PreprintCC BY-NC-ND 4.0arXiv

Chern's Conjecture with Constant Cubic Trace

  • Huixin Tan
  • Zizhou Tang
  • Yuquan Xie
  • Wenjiao Yan
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Abstract

We prove that the values set of S=|A|2 attained by closed embedded minimal hypersurfaces in 𝕊n+1(1) with constant S and constant f3=tr(A3) is locally finite, where A denotes the shape operator. Neither the topology of the hypersurface nor the value of f3 is fixed.

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Cite

BibTeXRIS
BibTeX
@misc{tan2026cherns,
  title = {{Chern's Conjecture with Constant Cubic Trace}},
  author = {Huixin Tan and Zizhou Tang and Yuquan Xie and Wenjiao Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03711},
  eprint = {2609.03711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03711},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Chern's Conjecture with Constant Cubic Trace
AU  - Huixin Tan
AU  - Zizhou Tang
AU  - Yuquan Xie
AU  - Wenjiao Yan
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03711
UR  - https://arxiv.org/abs/2609.03711
AB  - We prove that the values set of S=|A|^2 attained by closed embedded minimal hypersurfaces in 𝕊^n+1(1) with constant S and constant f_3=tr(A^3) is locally finite, where A denotes the shape operator. Neither the topology of the hypersurface nor the value of f_3 is fixed.
ER  -