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Abstract
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear diffusions. Our results apply in particular to Ricci flow, where they yield a local monotone quantity directly analogous to Perelman's reduced volume V and a local identity related to Perelman's average energy F.
Received: 2006-08-18
Revised: 2007-01-08
Published Online: 2008-05-13
Published in Print: 2008-March
© Walter de Gruyter
