Let be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial homology. We show that the entropy of is greater than or equal to the entropy of a round -sphere, and that if equality holds, then is a round -sphere in .
"Sharp entropy bounds for self-shrinkers in mean curvature flow." Geom. Topol. 23 (3) 1611 - 1619, 2019. https://doi.org/10.2140/gt.2019.23.1611