On the l-Function and the Reduced Volume of Perelman I

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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.
This paper has been available at the author's website. We post it here to make it easier to access. To appear in Transactions of American Mathematical Society

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