Time: 2:00-4:00pm, July 21

Place: Quan Zhai 9, BICMR

Speaker: Dr Lu Wang

Abstract: Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinkers in R^{n+1}, the entropy is uniquely minimized at the round sphere. They conjectured that, for dimension between 2 and 6, the round sphere minimizes the entropy among all closed smooth hypersurfaces. Joint with Jacob Bernstein, we prove their conjecture via an appropriate weak mean curvature flow. For these dimensions, our approach also gives a new proof of the main result of Colding-Ilmanen-Minicozzi-White and extends its conclusions to compact singular self-shrinkers.