Journal of the European Mathematical Society· 2026Q1
On the rigidity of Ricci shrinkers
- 11citations
- Q1SCImago
- 2026year
Short summary
The generalized cylinder N^{n} \times \mathbb{R}^{m-n} (or its quotient) is proven to be rigid in the space of Ricci shrinkers under the pointed Gromov–Hausdorff topology, where N is a stable Einstein manifold with an order 3 obstruction.
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Key points
- The generalized cylinder N^{n} \times \mathbb{R}^{m-n} is rigid in the space of Ricci shrinkers under the pointed Gromov–Hausdorff topology.
- N is defined as a stable Einstein manifold with an order 3 obstruction.
- The proof utilizes quantitative characterization of compact Ricci shrinker rigidity and mixed-order rigidity inequalities.
- As an application, the uniqueness of tangent flow for general compact Ricci flows is proven if one tangent flow is a generalized cylinder.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal of the European Mathematical Society, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics