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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 journal › Article › peer-review

Harvard

Burago, D & Ivanov, S 2012, 'Minimality of planes in normed spaces', Geometric and Functional Analysis, vol. 22, no. 3, pp. 627-638. https://doi.org/10.1007/s00039-012-0170-y

APA

Burago, D., & Ivanov, S. (2012). Minimality of planes in normed spaces. Geometric and Functional Analysis, 22(3), 627-638. https://doi.org/10.1007/s00039-012-0170-y

Vancouver

Burago D, Ivanov S. Minimality of planes in normed spaces. Geometric and Functional Analysis. 2012 Sep 1;22(3):627-638. https://doi.org/10.1007/s00039-012-0170-y

Author

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

BibTeX

@article{bca03120b33048e290185be84d856917,
title = "Minimality of planes in normed spaces",
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.",
keywords = "Busemann-Hausdorff surface area, convexity, ellipticity",
author = "Dmitri Burago and Sergei Ivanov",
year = "2012",
month = sep,
day = "1",
doi = "10.1007/s00039-012-0170-y",
language = "English",
volume = "22",
pages = "627--638",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - Minimality of planes in normed spaces

AU - Burago, Dmitri

AU - Ivanov, Sergei

PY - 2012/9/1

Y1 - 2012/9/1

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.

KW - Busemann-Hausdorff surface area

KW - convexity

KW - ellipticity

UR - http://www.scopus.com/inward/record.url?scp=84866929261&partnerID=8YFLogxK

U2 - 10.1007/s00039-012-0170-y

DO - 10.1007/s00039-012-0170-y

M3 - Article

AN - SCOPUS:84866929261

VL - 22

SP - 627

EP - 638

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 3

ER -

ID: 49983330