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On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II. / Kopylov, Anatolii Pavlovich.
в: Сибирские электронные математические известия, Том 14, 01.01.2017, стр. 986-993.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II
AU - Kopylov, Anatolii Pavlovich
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We prove the theorem on the unique determination of a strictly convex domain in ℝn, where n ≥ 2, in the class of all n- dimensional domains by the condition of the local isometry of the Hausdorff boundaries in the relative metrics, which is a generalization of A. D. Aleksandrov's theorem on the unique determination of a strictly convex domain by the condition of the (global) isometry of the boundaries in the relative metrics. We also prove that, in the cases of a plane domain U with nonsmooth boundary and of a three-dimensional domain A with smooth boundary, the convexity of the domain is no longer necessary for its unique determination by the condition of the local isometry of the boundaries in the relative metrics.
AB - We prove the theorem on the unique determination of a strictly convex domain in ℝn, where n ≥ 2, in the class of all n- dimensional domains by the condition of the local isometry of the Hausdorff boundaries in the relative metrics, which is a generalization of A. D. Aleksandrov's theorem on the unique determination of a strictly convex domain by the condition of the (global) isometry of the boundaries in the relative metrics. We also prove that, in the cases of a plane domain U with nonsmooth boundary and of a three-dimensional domain A with smooth boundary, the convexity of the domain is no longer necessary for its unique determination by the condition of the local isometry of the boundaries in the relative metrics.
KW - Intrinsic metric
KW - Local isometry of the boundaries
KW - Relative metric of the boundary
KW - Strict convexity
KW - strict convexity
KW - relative metric of the boundary
KW - local isometry of the boundaries
KW - intrinsic metric
UR - http://www.scopus.com/inward/record.url?scp=85074639036&partnerID=8YFLogxK
U2 - 10.17377/semi.2017.14.083
DO - 10.17377/semi.2017.14.083
M3 - Article
AN - SCOPUS:85074639036
VL - 14
SP - 986
EP - 993
JO - Сибирские электронные математические известия
JF - Сибирские электронные математические известия
SN - 1813-3304
ER -
ID: 22320147