  The characterization of global solutions to the obstacle problems in
$\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied
over more than 90 years. In this paper we give a conclusive answer to this
problem by proving the following long-standing conjecture: The coincidence set
of a global solution to the obstacle problem is either a half-space, an
ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as
base.
