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arXiv · 1701.01989

The Rigidity of Ricci shrinkers of dimension four

Yu Li·Bing Wang
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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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Yu Li, Bing Wang. 2017-01-08. The Rigidity of Ricci shrinkers of dimension four. https://arxiv.org/abs/1701.01989

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