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Transactions of the American Mathematical Society

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The rigidity of Ricci shrinkers of dimension four


Authors: Yu Li and Bing Wang
Journal: Trans. Amer. Math. Soc. 371 (2019), 6949-6972
MSC (2010): Primary 53C24
DOI: https://doi.org/10.1090/tran/7539
Published electronically: February 21, 2019
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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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Additional Information

Yu Li
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: yu.li.4@stonybrook.edu

Bing Wang
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, No. 96 Jinzhai Road, Hefei, Anhui Providence, 230036, China; and Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin 53706
Email: bwang@math.wisc.edu

DOI: https://doi.org/10.1090/tran/7539
Received by editor(s): February 23, 2017
Received by editor(s) in revised form: December 28, 2017
Published electronically: February 21, 2019
Additional Notes: Both authors were partially supported by NSF grant DMS-1510401. They also acknowledge the invitation to MSRI Berkeley in spring 2016 supported by NSF grant DMS-1440140, where part of this work was carried out.
Article copyright: © Copyright 2019 American Mathematical Society