Abstract
In this paper, the uniqueness of the dual Minkowski problem for the dual area measure is established via the dual Minkowski inequality and the dual log-Minkowski inequality. For real q>n−1, it is proved that the weak convergence of the q-th dual area measure implies the convergence of the corresponding convex bodies in the Hausdorff metric and that the solution to the dual Minkowski problem is continuous with respect to q.
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