Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Minimality of planes in normed spaces. / Burago, Dmitri; Ivanov, Sergei.
в: Geometric and Functional Analysis, Том 22, № 3, 01.09.2012, стр. 627-638.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
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