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math.DG2003★ 607 cited
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
Grisha Perelman
Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci f…
math.DG2003★ 994 cited
Ricci flow with surgery on three-manifolds
Grisha Perelman
This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-p…
math.DG2002
The entropy formula for the Ricci flow and its geometric applications
Grisha Perelman
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. S…