The transverse entropy functional and the Sasaki-Ricci flow
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- by Tristan C. Collins PDF
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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.References
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Additional Information
- Tristan C. Collins
- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 1003845
- Email: tcollins@math.columbia.edu
- Received by editor(s): March 31, 2011
- Published electronically: September 19, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3003265