Smooth geometric evolutions of hypersurfaces
微分几何
2007-05-23 v1 偏微分方程分析
摘要
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.
引用
@article{arxiv.math/0103016,
title = {Smooth geometric evolutions of hypersurfaces},
author = {Carlo Mantegazza},
journal= {arXiv preprint arXiv:math/0103016},
year = {2007}
}
备注
34 pages