Minimality of planes in normed spaces

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 Λ 2V. The proof is based on a (probably) new inequality for the Euclidean area of a convex centrally-symmetric polygon.

Original languageEnglish (US)
Pages (from-to)627-638
Number of pages12
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Sep 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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