A local regularity theorem for mean curvature flow (Q815037)

This paper concerns the regularity theory for the mean curvature flow and its generalizations including varifold flows. Although the main result consists in obtaining ``curvature bounds for the mean curvature flow and other related flows in regions of space-times where the Gaussian densities are close to 1'' the paper presents a general theory which can be applied ``up to and including the time at which singularities first occur in any classical mean curvature flow''. Moreover it is indicated how this theory is extended to the case of varifold flows which are weak limits of smooth mean curvature flows or flows constructed by Ilmanen's elliptic regularization procedure.