  The present paper introduces a new class of geometric measures, the k-th
(p,q)-mixed curvature measures, and a natural
correspondence-(p,q)-Christoffel-Minkowski problem is proposed. The
(p,q)-Christoffel-Minkowski problem posed here can be regarded as a natural
generalization of the L_p Christoffel-Minkowski problem and Lp dual Minkowski
problem.
  We investigate and arrive at the existence of smooth solution to the
(p,q)-Christoffel-Minkowski problem by a type of expanding curvature flow.
Furthermore, the uniqueness result of solutions to the
(p,q)-Christoffel-Minkowski problem shall be discussed.
