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Symmetric Self-Shrinkers for the Fractional Mean Curvature Flow

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Abstract

We show existence of homothetically shrinking solutions of the fractional mean curvature flow, whose boundary consists in a prescribed number of concentric spheres. We prove that all these solutions, except from the ball, are dynamically unstable.

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Acknowledgements

The authors are members of INDAM-GNAMPA. The second author was partially supported by the University of Pisa Project PRA 2017 Problemi di ottimizzazione e di evoluzione in ambito variazionale.

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Authors and Affiliations

  1. Department of Statistical Sciences, University of Padova, Via Cesare Battisti 141, 35121, Padua, Italy

    Annalisa Cesaroni

  2. Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Matteo Novaga

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  1. Annalisa Cesaroni
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  2. Matteo Novaga
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Correspondence to Matteo Novaga.

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Cesaroni, A., Novaga, M. Symmetric Self-Shrinkers for the Fractional Mean Curvature Flow. J Geom Anal 30, 3698–3715 (2020). https://doi.org/10.1007/s12220-019-00214-2

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  • DOI: https://doi.org/10.1007/s12220-019-00214-2

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