Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow
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Author(s)
Deruelle, Alix
Ozuch, Tristan
Date Issued
January 12, 2023
Publisher
Springer Berlin Heidelberg
Citation
Calculus of Variations and Partial Differential Equations. 2023 Jan 12;62(3):84
Version
Author's final manuscript
Abstract
Abstract
We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for a variation of Perelman’s
$$\lambda $$
λ
functional adapted to the ALE situation and denoted
$$\lambda _{{\text {ALE}}}$$
λ
ALE
. This functional was introduced by the authors in a recent work and it has been proven that it satisfies a good enough Łojasiewicz inequality at least in neighborhoods of integrable ALE Ricci-flat metrics in dimension larger than or equal to 5.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00526-022-02403-4
