The Gaussian Minkowski problem is generalized to epigraphs of convex functions, and existence of convex functions realizing prescribed Gaussian moment measures is established under mild conditions.
Cordero-Erausquin, B
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The Gaussian Minkowski problem for epigraphs of convex functions
The Gaussian Minkowski problem is generalized to epigraphs of convex functions, and existence of convex functions realizing prescribed Gaussian moment measures is established under mild conditions.