Local monotonicity and mean value formulas for evolving Riemannian manifolds

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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.

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Differential Geometry, Analysis of PDEs, 53C44, 58J35, 35K55

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http://salesiana.dossiersoluciones.com/handle/123456789/115473

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608470
 http://arxiv.org/abs/math/0608470

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arXiv