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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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


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
  • ORCID: setImmediate$0.0885756173184169$3
  • Email:
  • 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
  • MR Author ID: 843464
  • Email:
  • 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 6949-6972
  • MSC (2010): Primary 53C24
  • DOI:
  • MathSciNet review: 3939566