An improved result on Chern conjecture

@misc{cheng2026improved,
  title = {{An improved result on Chern conjecture}},
  author = {Qing-Ming Cheng and Fengjiang Li and Guoxin Wei and Jiabin Yin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05276},
  eprint = {2610.05276},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05276},
}

TY  - UNPB
TI  - An improved result on Chern conjecture
AU  - Qing-Ming Cheng
AU  - Fengjiang Li
AU  - Guoxin Wei
AU  - Jiabin Yin
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.05276
UR  - https://arxiv.org/abs/2610.05276
AB  - Let X: M^n→ 𝕊^n+1(1) be a closed minimal hypersurface with constant scalar curvature. Chern conjecture says that a closed minimal hypersurface with constant scalar curvature, S≥ 2n if S>n, where S is the squared norm of the second fundamental form. As a partial result, Peng-Terng \cite{pt1, pt2}, Yang-Cheng \cite{yc1, yc2, yc3} and Suh-Yang \cite{sy} obtained that if S>n, then S>n+ 3/7n. Recently, Chen \cite{c} has proved S>n+26/59n if S>n. Since resolving Chern conjecture is a hard problem, as a midway for resolving Chern conjecture, one wants to prove S>n+1/2 n if S>n. In this paper, we give a positive solution for this midway problem. We should remark that our topological condition is complete which is weaker than closed in Chen \cite{c}.
ER  -