Stability of ALE Ricci-flat manifolds under Ricci flow

Abstract

We prove that if an ALE Ricci-flat manifold $(M,g)$ is linearly stable and integrable, it is dynamically stable under Ricci flow, i.e. any Ricci flow starting close to g exists for all time and converges modulo diffeomorphism to an ALE Ricci-flat metric close to $g$. By adapting Tian's approach in the closed case, we show that integrability holds for ALE Calabi-Yau manifolds which implies that they are dynamically stable.

35 pages, final version, to appear in J. Geom. Anal

References in corpus (1)

• Stability and instability of Ricci solitons

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