Communications in Analysis and Geometry

Volume 28 (2020)

Number 2

Stability of Einstein metrics under Ricci flow

Pages: 351 – 394



Klaus Kröncke (Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany)


We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete characterization 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.

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Received 14 January 2016

Accepted 15 November 2017

Published 6 May 2020