Abstract
We prove that the set of smooth,
π
-periodic, positive functions on the unit circle for which the
L
−2
Minkowski problem is solvable is dense in the set of all smooth,
π
-periodic, positive functions on the unit circle with respect to the
L
∞
norm. Furthermore, we obtain a necessary condition on the solvability of the even
L
−2
Minkowski problem. At the end, we prove uniqueness of the solutions up to an affine linear transformation.