Existence for all real p (with symmetry in some cases) and uniqueness for p ≥ 1 under concavity are proved for the weighted L^p Minkowski problem with rotationally invariant measures, plus small-mass results via degree theory.
Cone-volume measure of g eneral centered convex bodies
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The Weighted $L^p$ Minkowski Problem
Existence for all real p (with symmetry in some cases) and uniqueness for p ≥ 1 under concavity are proved for the weighted L^p Minkowski problem with rotationally invariant measures, plus small-mass results via degree theory.