  We consider the gradient flow of hypersurfaces immersed in the Euclidean
space associated to geometric energy functionals.
  We show that for particular functionals depending by higher covariant
derivatives of the curvature, singularities in finite time cannot occur during
the evolution.
  Such geometric functionals are related to similar ones proposed by Ennio De
Giorgi, who conjectured for them an analogous regularity result.
