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Dynamical stability and instability of Ricci-flat metrics

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Abstract

In this short article, we improve the dynamical stability and instability results for Ricci-flat metrics under Ricci flow proved by Sesum (Duke Math J 133:1–26, 2006) and Haslhofer (Calc Var Partial Differ Equ 45:481–504, 2012), getting rid of the integrability assumption.

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Acknowledgments

We thank Felix Schulze and Leon Simon for discussions on related issues, and the referee for helpful comments. RM was financially supported by an Imperial College Junior Research Fellowship.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Robert Haslhofer

  2. School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Reto Müller

Authors
  1. Robert Haslhofer
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  2. Reto Müller
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Correspondence to Robert Haslhofer.

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Haslhofer, R., Müller, R. Dynamical stability and instability of Ricci-flat metrics. Math. Ann. 360, 547–553 (2014). https://doi.org/10.1007/s00208-014-1047-1

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  • DOI: https://doi.org/10.1007/s00208-014-1047-1

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