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A note on the compactness theorem for 4d Ricci shrinkers


Authors: Robert Haslhofer and Reto Müller
Journal: Proc. Amer. Math. Soc. 143 (2015), 4433-4437
MSC (2010): Primary 53C25, 53C44
DOI: https://doi.org/10.1090/proc/12648
Published electronically: May 20, 2015
MathSciNet review: 3373942
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Abstract: In a previous work published in 2011, we proved an orbifold
Cheeger-Gromov compactness theorem for complete 4d Ricci shrinkers with a lower bound for the entropy, an upper bound for the Euler characteristic, and a lower bound for the gradient of the potential at large distances. In this note, we show that the last two assumptions in fact can be removed. The key ingredient is a recent estimate of Cheeger-Naber (2014).


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Additional Information

Robert Haslhofer
Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
Email: robert.haslhofer@cims.nyu.edu

Reto Müller
Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
Email: r.mueller@qmul.ac.uk

DOI: https://doi.org/10.1090/proc/12648
Received by editor(s): July 22, 2014
Published electronically: May 20, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society