Limit shape of the cross-section of shrinking doughnuts
We discuss the asymptotic behaviour of symmetric tori which are shrinking to a circle by the mean curvature flow. Employing the backward heat kernel analysis we show that the limit shape of its cross-section is a circle. The assumption we set is that the isoperimetric ratio of the generating curve remains bounded as shrinking, which follows in particular from the convexity of curves.
scientific article; zbMATH DE number 469079