Conformal solitons to the mean curvature flow and minimal submanifolds

Authors

  • C. Arezzo,

    Corresponding author
    1. The Abdus Salam International Centre for Theoretical Physics, Trieste 34100, Italy. Phone: +39,040,2240,202, Fax: +39,040,2240,4103
    • The Abdus Salam International Centre for Theoretical Physics, Trieste 34100, Italy. Phone: +39,040,2240,255, Fax: +39,040,2240,410
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  • J. Sun

    1. The Abdus Salam International Centre for Theoretical Physics, Trieste 34100, Italy. Phone: +39,040,2240,202, Fax: +39,040,2240,4103
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Abstract

In this note we prove a correspondence, first found by Smoczyk in the hypersurface case, between conformal solitons to the mean curvature flow in an ambient manifold N and minimal submanifolds in a different space equation image. This naturally leads to a new natural stability notion for conformal solitons. We show that this corresponds to the recent Colding-Minicozzi's F-stability for codimension one self-shrinkers in euclidean space. In this spirit we can give some classification results for stable conformal solitons, answering two questions of Smoczyk.

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