Calculus of Variations and Geometric Measure Theory

S. Delladio

A criterion for $C^2$-rectifiability of sets

created on 14 Dec 2001
modified on 03 Feb 2004


Published Paper

Inserted: 14 dec 2001
Last Updated: 3 feb 2004

Journal: Ann. Mat. Pura ed Appl.
Volume: 182
Number: 3
Pages: 357-373
Year: 2003


The following result is proved: Let $M$ be a $n$-dimensional $C^1$-submanifold of $R^N$ which is domain of a given $\Lambda^n(R^N)$-valued map $\eta$ of class $C^1$. Then the subset of $M$ at points of which $\eta$ is nonzero, simple and tangent to $M$ is $C^2$ rectifiable. As a corollary we get a criterion for $C^2$-rectifiability of sets.

Keywords: Rectifiable sets, C^2 rectifiability, sets with generalized curvature