The rigidity of Ricci shrinkers of dimension four

Li, Yu; Wang, Bing

doi:10.1090/tran/7539

The rigidity of Ricci shrinkers of dimension four
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by Yu Li and Bing Wang PDF

Trans. Amer. Math. Soc. 371 (2019), 6949-6972 Request permission

Abstract:

In dimension $4$, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality under the pointed-Gromov-Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinkers satisfying some natural geometric properties.

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