Elasticae and inradius
Résumé
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int_{\partial\Om} k^2(s)\,ds$
where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problem
of $E(\Om)$ with a constraint on the inradius of $\Om$. By contrast with all the other minimization problems
involving this elastic energy (with a perimeter, area, diameter or circumradius constraints) for which the
solution is always the disk, we prove here that the solution of this minimization problem is not the disk and we completely characterize
it in terms of elementary functions.
Domaines
Géométrie différentielle [math.DG]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...