Uniqueness and stability of singular Ricci flows in higher dimensions
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- by Robert Haslhofer PDF
- Proc. Amer. Math. Soc. 150 (2022), 5433-5437 Request permission
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 [ arXiv:2102.07180, 2021], and the maximum principle for the linearized Ricci-DeTurck flow on locally conformally flat manifolds due to Chen and Wu [Differential Geom. Appl. 46 (2016), pp. 108–118].References
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Additional Information
- Robert Haslhofer
- Affiliation: Department of Mathematics, University of Toronto, 40 St George Street, Toronto, Ontario M5S 2E4, Canada
- MR Author ID: 949022
- Email: roberth@math.toronto.edu
- Received by editor(s): January 13, 2022
- Published electronically: September 9, 2022
- Additional Notes: This research was supported by an NSERC Discovery Grant (RGPIN-2016-04331) and a Sloan Research Fellowship.
- Communicated by: Jiaping Wang
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5433-5437
- MSC (2020): Primary 53E20
- DOI: https://doi.org/10.1090/proc/16108