Minimality of planes in normed spaces

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 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
Volume22
Issue number3
DOIs
StatePublished - Sep 1 2012

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Minimality
Normed Space
Hausdorff Measure
Polygon
Euclidean
Subspace

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Cite this

Burago, Dmitri ; Ivanov, Sergei. / Minimality of planes in normed spaces. In: Geometric and Functional Analysis. 2012 ; Vol. 22, No. 3. pp. 627-638.
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Minimality of planes in normed spaces. / Burago, Dmitri; Ivanov, Sergei.

In: Geometric and Functional Analysis, Vol. 22, No. 3, 01.09.2012, p. 627-638.

Research output: Contribution to journalArticle

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