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Ancient solutions to mean curvature flow for isoparametric submanifolds

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Abstract

Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied in Liu and Terng (Duke Math J 147(1):157–179, 2009). In this paper, we will show that all these solutions are ancient solutions and study their limits as time goes to negative infinity. We also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the Chern’s conjecture on the norm of the second fundamental forms of minimal hypersurfaces in spheres.

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Authors and Affiliations

  1. Beijing International Center for Mathematical Research and School of Mathematical Sciences, Peking University, Beijing, China

    Xiaobo Liu

  2. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697-3875, USA

    Chuu-Lian Terng

Authors
  1. Xiaobo Liu
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  2. Chuu-Lian Terng
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Correspondence to Xiaobo Liu.

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Communicated by F.C. Marques.

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X. Liu: Research was partially supported by NSFC Grants 11890662, 11890660, and 11431001.

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Liu, X., Terng, CL. Ancient solutions to mean curvature flow for isoparametric submanifolds. Math. Ann. 378, 289–315 (2020). https://doi.org/10.1007/s00208-020-02055-9

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  • DOI: https://doi.org/10.1007/s00208-020-02055-9

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