Minimality of planes in normed spaces |
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| Authors: | Dmitri Burago Sergei Ivanov |
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| Affiliation: | 1. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA
2. St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia
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| Abstract: | 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 Λ2 V. The proof is based on a (probably) new inequality for the Euclidean area of a convex centrally-symmetric polygon. |
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