Calculus of Variations and Geometric Measure Theory

P. Cannarsa - M. O. Czarnecki

Minkowski content for reachable sets

created by cannarsa on 23 Apr 2008



Inserted: 23 apr 2008

Year: 2008


In 1955, Martin Kneser showed that the Minkowski content of a compact $p$-rectifiable subset $M$ of $R^n$ is equal to its $p$-Hausdorff measure. We extend his result to the reachable sets of a linear control system $$ \dot{x}= f(x) \> u, $$ and we give an interpretation in terms of Riemannian distance.

Keywords: Minkowski content, tubes, reachable sets