Mean curvature flow without singularities
  We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to smoothly flow through singularities by studying graphical mean curvature flow with one additional dimension. 
Mariel S\'aez Trumper, Oliver C. Schn\"urer
math.DG math.AP