Perelman's l-distrance

This talk is a preparation of the necessary tools for proving the non-collapsing results. The L-length defined by Perelman is the analog of an energy path, but defined in a Riemannian manifold context. The length is used to define the l reduced distance and later on, the reduced volume. So far the properties of the l-length have two applications in the proof of the Poincare conjecture. Associated with the notion of reduced volume, they are used to prove non-collapsing results and also to study the K- solutions.