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The Ricci flow under almost non-negative curvature conditions.
- Source :
-
Inventiones Mathematicae . Jul2019, Vol. 217 Issue 1, p95-126. 32p. - Publication Year :
- 2019
-
Abstract
- We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than - 1 can be evolved by the Ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than - C . Here the time of existence and the constant C only depend on the dimension and the degree of non-collapsedness. We obtain similar generalizations for other invariant curvature conditions, including positive biholomorphic curvature in the Kähler case. We also get a local version of the main theorem. As an application of our almost preservation results we deduce a variety of gap and smoothing results of independent interest, including a classification for non-collapsed manifolds with almost non-negative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds. We also obtain a short-time existence result for the Ricci flow on open manifolds with almost non-negative curvature (without requiring upper curvature bounds). [ABSTRACT FROM AUTHOR]
- Subjects :
- *RICCI flow
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 00209910
- Volume :
- 217
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Inventiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 136787749
- Full Text :
- https://doi.org/10.1007/s00222-019-00864-7