Existence of Optimal Flat Ribbons.

We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in R3 can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish.

A minimising movement scheme for the p-elastic energy of curves.

We prove short-time existence for the negative L 2 -gradient flow of the p-elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy's invariance under curve reparametrisations, we write the evolving curves as approximate normal graphs over a fixed smooth curve. This enables us to establish short-time existence and give a lower bound on the solution's lifetime that depends only on the W 2 , p -Sobolev norm of the initial data.