Calculus of Variations and Geometric Measure Theory

S. Delladio

The projection of a rectifiable Legendrian set is $C^2$-rectifiable: a simplified proof

created on 18 Sep 2001
modified on 03 Feb 2004


Published Paper

Inserted: 18 sep 2001
Last Updated: 3 feb 2004

Journal: Proc. Royal Soc. Edinburgh.
Volume: 133
Pages: 85-96
Year: 2003


We provide a simplified proof of the following well-known theorem: {\it The projection to $R^{n+1}$ of a $n$-dimensional rectifiable Legendrian subset of $R^{n+1}\times S^n$ is $C^2$-rectifiable.} Such a result generalizes the following simple fact: {\it Let $M$ be a hypersurface whose Gauss map has graph of class $C^1$. Then $M$ is of class $C^2$.}

Keywords: Geometric measure theory, Legendrian sets