This content will become publicly available on July 14, 2023
 Award ID(s):
 1907391
 Publication Date:
 NSFPAR ID:
 10349919
 Journal Name:
 Communications of the American Mathematical Society
 Volume:
 2
 Issue:
 5
 Page Range or eLocationID:
 172 to 231
 ISSN:
 26923688
 Sponsoring Org:
 National Science Foundation
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The principle of convergence stability for geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial state g0 exists for all time and converges to a stable fixed point, then the flows of solutions that start near g0 also converge to fixed points. We show this in the case of the Ricci flow, carefully proving the continuous dependence on initial conditions. Symmetry assumptions on initial geometries are often made to simplify geometric flow equations. As an application of our results, we extend known convergence results to open sets of these initial data, which contain geometries with no symmetries.

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