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Local monotonicity and mean value formulas for evolving Riemannian manifolds
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Ecker, Klaus, Knopf, Dan, Ni, Lei and Topping, Peter (2008) Local monotonicity and mean value formulas for evolving Riemannian manifolds. Journal fur die reine und angewandte Mathematik, Vol.2008 (No.616). pp. 89-130. doi:10.1515/CRELLE.2008.019 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/CRELLE.2008.019
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) over tilde and a local identity related to Perelman's average energy F.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal fur die reine und angewandte Mathematik | ||||
Publisher: | Walter de Gruyter & Co | ||||
ISSN: | 0075-4102 | ||||
Official Date: | March 2008 | ||||
Dates: |
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Volume: | Vol.2008 | ||||
Number: | No.616 | ||||
Number of Pages: | 42 | ||||
Page Range: | pp. 89-130 | ||||
DOI: | 10.1515/CRELLE.2008.019 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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