Some Properties of the Distance Function and a Conjecture of De Giorgi
Analysis of PDEs
2007-05-23 v1 Functional Analysis
Abstract
We analyse the geometric properties of the high derivatives of the distance function from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its covariant derivatives of independent interest. As an application we prove a conjecture of Ennio De Giorgi on the evolution of submanifolds of the Euclidean space by the gradient of functionals depending on the derivatives of the distance function.
Keywords
Cite
@article{arxiv.math/0306141,
title = {Some Properties of the Distance Function and a Conjecture of De Giorgi},
author = {Manolo Eminenti and Carlo Mantegazza},
journal= {arXiv preprint arXiv:math/0306141},
year = {2007}
}