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Uniqueness and stability of singular Ricci flows in higher dimensions
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abstract
In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical neighborhood property. In particular, this gives a canonical evolution through singularities for manifolds with positive isotropic curvature. The new ingredients we use are the recent classification of higher dimensional $\kappa$-solutions by Brendle, Daskalopoulos, Naff and Sesum, and the maximum principle for the linearized Ricci-DeTurck flow on locally conformally flat manifolds due to Chen and Wu.
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Cited by 1 Pith paper
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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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