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On the $ l$-function and the reduced volume of Perelman I

Author(s): Rugang Ye
Journal: Trans. Amer. Math. Soc. 360 (2008), 507-531.
MSC (2000): Primary 53C20, 53C21
Posted: August 6, 2007
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Abstract: The main purpose of this paper is to present a number of analytic and geometric properties of the $ l$-function and the reduced volume of Perelman, including in particular the monotonicity, the upper bound and the rigidities of the reduced volume.

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B. Kleiner and J. Lott, Notes on Perelman's papers, www.math.lsa.umich.edu/research/ ricciflow/perelman.html

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G. Perelman, Ricci flow with surgeries on three-manifolds, arXiv:math.DG/0303109.

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R. Ye, On the $ l$-function and the reduced volume of Perelman.

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R. Ye, On the $ l$-function and the reduced volume of Perelman II, this issue.

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R. Ye, Notes on convex functions on Riemannian manifolds.

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Additional Information:

Rugang Ye
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: yer@math.ucsb.edu

DOI: 10.1090/S0002-9947-07-04405-4
PII: S 0002-9947(07)04405-4
Received by editor(s): May 20, 2006
Received by editor(s) in revised form: September 1, 2006
Posted: August 6, 2007
Copyright of article: Copyright 2007, Rugang Ye

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