For the Finsler p-Laplacian torsion problem, a nonzero finite measure is an anisotropic p-torsional measure of a convex body iff its centroid is the origin and it is not concentrated on a closed hemisphere; the log version holds under a subspace mass inequality.
Andrews, Volume-preserving anisotropic mean curvature flow, Indiana Univ
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Minkowski problem of anisotropic p-torsional rigidity
For the Finsler p-Laplacian torsion problem, a nonzero finite measure is an anisotropic p-torsional measure of a convex body iff its centroid is the origin and it is not concentrated on a closed hemisphere; the log version holds under a subspace mass inequality.