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arXiv · 2110.03412

Uniqueness and stability of singular Ricci flows in higher dimensions

Robert Haslhofer
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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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Robert Haslhofer. 2021-10-07. Uniqueness and stability of singular Ricci flows in higher dimensions. https://arxiv.org/abs/2110.03412

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