Dynamical (in)stability of Ricci-flat ALE metrics along Ricci flow

Alix Deruelle; Tristan Ozuch

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Dynamical (in)stability of Ricci-flat ALE metrics along Ricci flow

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arxiv 2104.10630 v1 pith:HJWTZHIN submitted 2021-04-21 math.DG

Alix Deruelle , Tristan Ozuch This is my paper · ORCID

classification math.DG

keywords metricsricci-flatfunctionalinequalitylambdalojasiewiczstabilityadapted

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abstract

We study the stability and instability of ALE Ricci-flat metrics around which a Lojasiewicz inequality is satisfied for a variation of Perelman's $\lambda$-functional adapted to the ALE situation and denoted $\lambda_{\operatorname{ALE}}$. This functional was introduced by the authors in a recent work and it has been proven that it satisfies a good enough Lojasiewicz inequality at least in neighborhoods of integrable ALE Ricci-flat metrics in dimension larger than or equal to 5.

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