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Some curvature pinching results for Riemannian manifolds with density


Author: William Wylie
Journal: Proc. Amer. Math. Soc. 144 (2016), 823-836
MSC (2010): Primary 53C25
DOI: https://doi.org/10.1090/proc/12853
Published electronically: August 26, 2015
MathSciNet review: 3430857
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Abstract: In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.


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Additional Information

William Wylie
Affiliation: Department of Mathematics, 215 Carnegie Building, Syracuse University, Syracuse, New York 13244
Email: wwylie@syr.edu

DOI: https://doi.org/10.1090/proc/12853
Received by editor(s): January 24, 2015
Published electronically: August 26, 2015
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society