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PreprintCC BY 4.0arXiv

Scalar curvature bounds and rigidity of Ricci shrinkers

  • Jianyu Ou
  • Guoqiang Wu
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Abstract

We prove that a complete noncompact gradient shrinking Ricci soliton of dimension at least two is a finite quotient of an Einstein cylinder if its scalar curvature is bounded below by the cylindrical value. The corresponding pointwise strict bound implies compactness. We also establish one-endedness criteria using curvature information at critical points of the potential, including degenerate ones, and obtain sharp one-endedness and rigidity results under global Ricci norm bounds.

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Cite

BibTeXRIS
BibTeX
@misc{ou2026scalar,
  title = {{Scalar curvature bounds and rigidity of Ricci shrinkers}},
  author = {Jianyu Ou and Guoqiang Wu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07381},
  eprint = {2611.07381},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07381},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Scalar curvature bounds and rigidity of Ricci shrinkers
AU  - Jianyu Ou
AU  - Guoqiang Wu
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07381
UR  - https://arxiv.org/abs/2611.07381
AB  - We prove that a complete noncompact gradient shrinking Ricci soliton of dimension at least two is a finite quotient of an Einstein cylinder if its scalar curvature is bounded below by the cylindrical value. The corresponding pointwise strict bound implies compactness. We also establish one-endedness criteria using curvature information at critical points of the potential, including degenerate ones, and obtain sharp one-endedness and rigidity results under global Ricci norm bounds.
ER  -