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The Rigidity of Ricci shrinkers of dimension four
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The Rigidity of Ricci shrinkers of dimension four
classification
math.DG
keywords
riccishrinkerscurvaturedimensionscalarapplicationsapproximatedbounded
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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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