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Lutwak, Yang and Zhang [23] introduced the concept of Lp dual curvaturemeasure for convex bodies and star bodies, and studied the Minkowski problem.We in this paper establish a new unified concept, in briefly, the (p,q)-mixedquermassintegrals, via (p,q)-dual mixed curvature measure, and further have adeep discussion on Minkowski problem with respect to the (p,q)-dual mixedcurvature measure. By the way, we derive at some important properties andgeometric inequalities for (p,q)-mixed quermassintegrals.

The Minkowski problem based on the (p,q)-mixed quermassintegrals