Convexity estimates for singularities of the mean curvature flow
Hypersurfaces moving along their mean curvature vector
typically develop singularities in finite time. The structure of such singularities
can be studied with rescaling techniques, and this lecture presents joint
work with Carlo Sinestrari (Rome) on the limiting shape of rescaled singularities.
In particular, it is shown that for mean convex initial data any smooth
rescaling of a singularity is weakly convex.
Spring 1999 meeting of the PNGS