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Convergence stability for Ricci flow on manifolds with bounded geometry.
- Source :
- Proceedings of the American Mathematical Society; Jan2024, Vol. 152 Issue 1, p435-446, 12p
- Publication Year :
- 2024
-
Abstract
- We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on recent work of Bahuaud, Guenther, Isenberg and Mazzeo where sectoriality for the generator of the Ricci-DeTurck flow is proved. We use this to prove that for initial metrics sufficiently close in Hölder norm to a rotationally symmetric asymptotically hyperbolic metric and satisfying a simple curvature condition, but a priori distant from the hyperbolic metric, Ricci flow converges to the hyperbolic metric. [ABSTRACT FROM AUTHOR]
- Subjects :
- RICCI flow
GEOMETRY
CURVATURE
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 152
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 173310838
- Full Text :
- https://doi.org/10.1090/proc/16593