Entropy Bounds for Self-Shrinkers with Symmetries

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.