Published Paper
(1998)
Authors:
Luigi Ambrosio - Carlo Mantegazza
Journal: J. Geom. Anal. [MathSciNet]
Volume: 8
Pages: 723-748
Abstract:
This paper is concerned with the relations between the
differential invariants of a smooth manifold embedded in the
Euclidean space and the square of the distance function
from the manifold. In particular, we are interested in
curvature invariants like the mean curvature vector and the
second fundamental form. We find that these invariants can
be computed in a very simple way using the third order
derivatives of the squared distance function.
Moreover, we study a general class of functionals
depending on the derivatives of the squared distance
function and we find an algorithm for the computation of the
Euler equation. Our class of functionals includes as
particular cases the well known Area functional, the integral
of the square of the quadratic norm of the second
fundamental form and the Willmore functional.![[PS]](/style/ps.png)
![[PDF]](/style/pdf.png)
[BibTeX Entry]
Available Files:
abstract.tex (abstract.ps, abstract.pdf)
paper.ps (paper.pdf)
