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The transverse entropy functional and the Sasaki-Ricci flow


Author: Tristan C. Collins
Journal: Trans. Amer. Math. Soc. 365 (2013), 1277-1303
MSC (2010): Primary 53C25, 53C44
DOI: https://doi.org/10.1090/S0002-9947-2012-05601-7
Published electronically: September 19, 2012
MathSciNet review: 3003265
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Abstract: We introduce two new functionals, inspired by the work of Perelman, which are monotonic along the Sasaki-Ricci flow. We relate their gradient flow, via diffeomorphisms preserving the foliated structure of the manifold, to the transverse Ricci flow. Finally, when the basic first Chern class is positive, we employ these new functionals to prove a uniform $ C^{0}$ bound for the transverse scalar curvature, and a uniform $ C^{1}$ bound for the transverse Ricci potential along the Sasaki-Ricci flow.


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Additional Information

Tristan C. Collins
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: tcollins@math.columbia.edu

DOI: https://doi.org/10.1090/S0002-9947-2012-05601-7
Received by editor(s): March 31, 2011
Published electronically: September 19, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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