As on arXiv
Abstract
In this paper, we establish the rigidity of the generalized cylinder , or a quotient thereof, in the space of Ricci shrinkers equipped with the pointed-Gromov-Hausdorff topology. Here, is a stable Einstein manifold that has an obstruction of order . 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.
Comments: v2: 76 pages, 2 figures; typos corrected, appendix updated and refined
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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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Rigidity of the round cylinders in Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”, “Hausdorff topology”, “pointed Gromov”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same authors Yu Li, Wenjia Zhang · Shared terms “Ricci shrinkers”, “Gromov Hausdorff”
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On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
Topics Limit spaces & RCD, Stability & uniqueness, Ricci solitons · Same authors Yu Li, Wenjia Zhang · Shared terms “Ricci shrinkers”, “pointed Gromov”, “Gromov Hausdorff”
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Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow
Topics Einstein metrics, Singularities, Stability & uniqueness · Same author Yu Li · Shared terms “generalized cylinder”, “tangent flow”, “obstruction”
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On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness
Topics Singularities, Stability & uniqueness, Ricci solitons · Same authors Yu Li, Wenjia Zhang · Shared terms “Ricci shrinkers”, “tangent flow”, “quantitative”
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Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Topics Stability & uniqueness, Ricci solitons · Same authors Yu Li, Wenjia Zhang · Shared terms “Ricci shrinkers”
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Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
Topics Singularities, Stability & uniqueness · Same author Yu Li · Shared terms “tangent flow”, “quotient thereof”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics Limit spaces & RCD, Singularities, Stability & uniqueness · Same author Yu Li · Shared terms “Ricci shrinkers”, “Gromov Hausdorff”, “pointed Gromov”
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