In his famous book on partial differential relations Gromov formulates an exercise concerning local deformations of solutions to open partial differential relations. We will explain the content of this fundamental assertion and sketch a proof.

In the sequel we will apply this general result in order

1) to inrease the excitement of Oktoberfest roller coasters without violating safety restrictions,

2) to construct C^{1,1}-Riemannian metrics which are positively curved „almost everywhere“ on arbitrary manifolds.

This talk is based on joint work with Christian Bär (Potsdam).