In this paper, we prove that the round cylinders are rigid in the space of Ricci shrinkers. Namely, any Ricci shrinker that is sufficiently close to Sⁿ⁻¹ × R in the pointed-Gromov-Hausdorff topology must itself be isometric to Sⁿ⁻¹ × R.
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Li et al. (2024) studied this question.
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