Minimality of planes in normed spaces

Details Minimality of planes in normed spaces Minimality of planes in normed spaces

2012-04-06

arxiv.org/abs/1204.1543v1

Mathematics

Metric Geometry

10 pages

Scientific paper

We prove that a region in a two-dimensional affine subspace of a normed space
$V$ 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 $\Lambda^2 V$. The proof is based on a (probably)
new inequality for the Euclidean area of a convex centrally-symmetric polygon.

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