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The centro-affine Minkowski problem for polytopes. (English) Zbl 1331.53016
Let \(\mu\) be a discrete measure on the unit sphere \(S^{n-1}\). A finite subset \(U\) of \(S^{n-1}\) is said to be in general position if any \(k\) elements of \(U\), \(1\leq k \leq n\), are linearly independent. The author proves that \(\mu\) is the centro-affine surface area measure of a polytope whose outer unit normals are in general position if and only if the support of \(\mu\) is in general position and not contained in a closed hemisphere.

MSC:
53A15 Affine differential geometry
52B11 \(n\)-dimensional polytopes
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