Some Properties of the Distance Function and a Conjecture of De Giorgi

Details Some Properties of the Distance Function and a Conjecture of De Giorgi Some Properties of the Distance Function and a Conjecture of De Giorgi

2003-06-08

arxiv.org/abs/math/0306141v1

J. Geom. Anal. 14 (2004), no. 2, 267-279

Mathematics

Analysis of PDEs

Scientific paper

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.

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