The paper gives necessary and sufficient conditions on a measure for the existence of G-invariant convex bodies solving the dual Minkowski problem for 0 < q ≤ n when G ⊂ O(n) has no nonzero fixed points.
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The Dual Minkowski Problem under Group Actions
The paper gives necessary and sufficient conditions on a measure for the existence of G-invariant convex bodies solving the dual Minkowski problem for 0 < q ≤ n when G ⊂ O(n) has no nonzero fixed points.