Minimality of planes in normed spaces

Dmitri Burago; Sergei Ivanov

doi:10.1007/s00039-012-0170-y

Minimality of planes in normed spaces

Dmitri Burago
, Sergei Ivanov

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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 language	English (US)
Pages (from-to)	627-638
Number of pages	12
Journal	Geometric and Functional Analysis
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/s00039-012-0170-y
State	Published - Sep 2012

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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

author = "Dmitri Burago and Sergei Ivanov",

note = "Funding Information: Keywords and phrases: Busemann–Hausdorff surface area, convexity, ellipticity Mathematics Subject Classification (1991): 52A21, 52A38, 52A40, 53C60 D. Burago was partially supported by NSF grant DMS-0905838. S. Ivanov was partially supported by RFBR grant 11-01-00302-a.",

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AU - Burago, Dmitri

AU - Ivanov, Sergei

N1 - Funding Information: Keywords and phrases: Busemann–Hausdorff surface area, convexity, ellipticity Mathematics Subject Classification (1991): 52A21, 52A38, 52A40, 53C60 D. Burago was partially supported by NSF grant DMS-0905838. S. Ivanov was partially supported by RFBR grant 11-01-00302-a.

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84866929261#tab=citedBy

U2 - 10.1007/s00039-012-0170-y

DO - 10.1007/s00039-012-0170-y

M3 - Article

AN - SCOPUS:84866929261

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Minimality of planes in normed spaces

Abstract

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