For p,q>1, an origin-symmetric convex body is claimed to exist whose normalized Lp Gaussian dual curvature measure matches any given even density measure, up to total mass scaling.
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The even Lp Gaussian dual Minkowski problem
For p,q>1, an origin-symmetric convex body is claimed to exist whose normalized Lp Gaussian dual curvature measure matches any given even density measure, up to total mass scaling.