  In the present paper we introduce a new generating function for outer
billiards in the plane. Using this generating function, we prove the following
rigidity result: if the vicinity of the smooth convex plane curve $\gamma$ of
positive curvature is foliated by continuous curves which are invariant under
outer billiard map, then the curve $\gamma$ must be an ellipse.
  In addition to the new generating function used in the proof, we also
overcome the noncompactness of the phase space by finding suitable weights in
the integral-geometric part of the proof. Thus, we reduce the result to the
Blaschke-Santalo inequality.
