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The local entropy along Ricci flow---Part B: the pseudo-locality theorems
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We localize the entropy functionals of G. Perelman and generalize his no-local-collapsing theorem and pseudo-locality theorem. Our generalization is technically inspired by further development of Li-Yau estimates along the Ricci flow. It has various applications, including to show the continuous dependence of the Ricci flow with respect to the initial metric in Gromov-Hausdorff topology with Ricci curvature bounded below, and to show the compactness of the moduli of K\"ahler manifolds with bounded scalar curvature and a rough locally almost Euclidean condition.
Forward citations
Cited by 2 Pith papers
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A note on a diffeomorphism criterion via long-time Ricci flow
A long-time Ricci flow with Ric ≥ -ψ/t and sufficiently large injectivity radius forces the manifold to be diffeomorphic to R^n, improving dimension-4 small-curvature-concentration results.
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Preserving curvature lower bounds when Ricci flowing non-smooth initial data
A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.
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