Local monotonicity and mean value formulas for evolving Riemannian manifolds

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dc.creatorEcker, Klaus
dc.creatorKnopf, Dan
dc.creatorNi, Lei
dc.creatorTopping, Peter
dc.date2006-08-18
dc.date.accessioned2026-07-07T07:21:55Z
dc.date.available2026-07-07T07:21:55Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0608470
dc.identifierhttp://arxiv.org/abs/math/0608470
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115473
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C44, 58J35, 35K55
dc.titleLocal monotonicity and mean value formulas for evolving Riemannian manifolds
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