Standard

On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II. / Kopylov, Anatolii Pavlovich.

In: Сибирские электронные математические известия, Vol. 14, 01.01.2017, p. 986-993.

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

Harvard

Kopylov, AP 2017, 'On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II', Сибирские электронные математические известия, vol. 14, pp. 986-993. https://doi.org/10.17377/semi.2017.14.083

APA

Kopylov, A. P. (2017). On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II. Сибирские электронные математические известия, 14, 986-993. https://doi.org/10.17377/semi.2017.14.083

Vancouver

Kopylov AP. On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II. Сибирские электронные математические известия. 2017 Jan 1;14:986-993. doi: 10.17377/semi.2017.14.083

Author

Kopylov, Anatolii Pavlovich. / On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II. In: Сибирские электронные математические известия. 2017 ; Vol. 14. pp. 986-993.

BibTeX

@article{c6fa48d26a394f189c299efb0fd0e4b3,
title = "On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II",
abstract = "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.",
keywords = "Intrinsic metric, Local isometry of the boundaries, Relative metric of the boundary, Strict convexity, strict convexity, relative metric of the boundary, local isometry of the boundaries, intrinsic metric",
author = "Kopylov, {Anatolii Pavlovich}",
year = "2017",
month = jan,
day = "1",
doi = "10.17377/semi.2017.14.083",
language = "English",
volume = "14",
pages = "986--993",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

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