Smooth geometric evolutions of hypersurfaces

Details Smooth geometric evolutions of hypersurfaces Smooth geometric evolutions of hypersurfaces

2001-03-03

arxiv.org/abs/math/0103016v1

Geom. Funct. Anal. 12 (2002), no. 1, 138-182

Mathematics

Differential Geometry

34 pages

Scientific paper

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.

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