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Entropy Bounds for Self-Shrinkers with Symmetries

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Abstract

In this work we derive explicit entropy bounds for two classes of closed self-shrinkers: the class of embedded closed self-shrinkers recently constructed in Riedler (in J Geom Anal 33(6):Paper No. 172, 2023) using isoparametric foliations of spheres, and the class of compact non-spherical immersed rotationally symmetric self-shrinkers. These bounds generalize the entropy bounds found in Ma, Muhammad, Møller (in J Reine Angew Math 793:239—259, 2022) on the space of complete embedded rotationally symmetric self-shrinkers.

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Notes

  1. In equation (4) of [28], the metric has the term \(e^{-r^2}\) instead of \(e^{-r^2/2}\) since they use a different scaling convention for self-shrinkers.

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Authors and Affiliations

  1. Department of Mathematics, Southern University of Science and Technology, No 1088, Xueyuan Rd., Xili, Nanshan District, Shenzhen, Guangdong, 518055, China

    John Man Shun Ma

  2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark

    Ali Muhammad

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  1. John Man Shun Ma
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Ma, J.M.S., Muhammad, A. Entropy Bounds for Self-Shrinkers with Symmetries. J Geom Anal 34, 36 (2024). https://doi.org/10.1007/s12220-023-01482-9

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