• Corpus ID: 7930618

The entropy formula for the Ricci flow and its geometric applications

  title={The entropy formula for the Ricci flow and its geometric applications},
  author={Grisha Perelman},
  journal={arXiv: Differential Geometry},
  • G. Perelman
  • Published 11 November 2002
  • Mathematics
  • arXiv: Differential Geometry
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. Several geometric applications are given. In particular, (1) Ricci flow, considered on the space of riemannian metrics modulo diffeomorphism and scaling, has no nontrivial periodic orbits (that is, other than fixed points); (2) In a region, where singularity is forming in finite time, the injectivity radius is… 
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