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Minimality of planes in normed spaces
We prove that a region in a two-dimensional affine subspace of a normed space
has the least 2-dimensional Hausdorff measure among all compact surfaces
with the same boundary. Furthermore, the 2-dimensional Hausdorff area density
admits a convex extension to . The proof is based on a (probably)
new inequality for the Euclidean area of a convex centrally-symmetric polygon.Comment: 10 pages, v2: minor changes according to referees' comments, to
appear in GAF
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