For every finite measure on the polar directions of a pointed cone, there exists a C-pseudo-cone whose Gaussian surface area measure equals that measure, with Gaussian co-volume no more than half the cone's.
Bakelman, Variational problems and elliptic Monge -Amp` ere equations, J
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The Gaussian-Minkowski problem for $C$-pseudo-cones
For every finite measure on the polar directions of a pointed cone, there exists a C-pseudo-cone whose Gaussian surface area measure equals that measure, with Gaussian co-volume no more than half the cone's.