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Peer-reviewedCC BYJournal of the European Mathematical Society

On the rigidity of Ricci shrinkers

  • Yu Li1,2
  • Wenjia Zhang3
  1. 1Hefei National Laboratory, P. R. China
  2. 2University of Science and Technology of China, Hefei
  3. 3University of Science and Technology of China, Hefei, P. R. China
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Abstract

We establish the rigidity of the generalized cylinder N^{n} \times \mathbb{R}^{m-n} , or a quotient thereof, in the space of Ricci shrinkers equipped with the pointed Gromov–Hausdorff topology. Here, N is a stable Einstein manifold that has an obstruction of order 3 . The proof is based on a quantitative characterization of the rigidity of compact Ricci shrinkers, a rigidity inequality of mixed orders on generalized cylinders, and the method of contraction and extension. As an application, we prove the uniqueness of the tangent flow for general compact Ricci flows under the assumption that one tangent flow is a generalized cylinder.

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Cite

BibTeXRIS
BibTeX
@article{li2026rigidity,
  title = {{On the rigidity of Ricci shrinkers}},
  author = {Yu Li and Wenjia Zhang},
  journal = {Journal of the European Mathematical Society},
  year = {2026},
  month = nov,
  doi = {10.4171/jems/1828},
  url = {https://doi.org/10.4171/jems/1828},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - On the rigidity of Ricci shrinkers
AU  - Yu Li
AU  - Wenjia Zhang
PY  - 2026
DA  - 2026/11/05
JO  - Journal of the European Mathematical Society
DO  - 10.4171/jems/1828
UR  - https://doi.org/10.4171/jems/1828
AB  - We establish the rigidity of the generalized cylinder N^{n} \times \mathbb{R}^{m-n} , or a quotient thereof, in the space of Ricci shrinkers equipped with the pointed Gromov–Hausdorff topology. Here, N is a stable Einstein manifold that has an obstruction of order 3 . The proof is based on a quantitative characterization of the rigidity of compact Ricci shrinkers, a rigidity inequality of mixed orders on generalized cylinders, and the method of contraction and extension. As an application, we prove the uniqueness of the tangent flow for general compact Ricci flows under the assumption that one tangent flow is a generalized cylinder.
SN  - 1435-9855
SN  - 1435-9863
ER  -