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arXiv:1312.2224 [math.DG]AbstractReferencesReviewsResources

Stability of Einstein metrics under Ricci flow

Klaus Kroencke

Published 2013-12-08, updated 2017-11-21Version 2

We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the Laplace spectrum. In particular, we prove dynamical stability of some classes of Einstein manifolds for which it was previously not known. Additionally, we show that the complex projective space with the Fubini-Study metric is surprisingly dynamically unstable.

Comments: 29 pages, final version with a modified title, to appear in Comm. Anal. Geom
Categories: math.DG, math.AP
Subjects: 53C25, 53C44
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