Bounding dimension of ambient space by density for mean curvature flow
  For an ancient solution of the mean curvature flow, we show that each time slice M_t is contained in an affine subspace with dimension bounded in terms of the density and the dimension of the evolving submanifold. Recall that an ancient solution is a family M_t that evolves under mean curvature flow for all negative time t. 
Maria Calle