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Problems of unique determination of domains by the relative metrics on their boundaries. / Kopylov, A. P.

In: Lobachevskii Journal of Mathematics, Vol. 38, No. 3, 01.05.2017, p. 476-487.

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

Harvard

Kopylov, AP 2017, 'Problems of unique determination of domains by the relative metrics on their boundaries', Lobachevskii Journal of Mathematics, vol. 38, no. 3, pp. 476-487. https://doi.org/10.1134/S1995080217030179

APA

Kopylov, A. P. (2017). Problems of unique determination of domains by the relative metrics on their boundaries. Lobachevskii Journal of Mathematics, 38(3), 476-487. https://doi.org/10.1134/S1995080217030179

Vancouver

Kopylov AP. Problems of unique determination of domains by the relative metrics on their boundaries. Lobachevskii Journal of Mathematics. 2017 May 1;38(3):476-487. doi: 10.1134/S1995080217030179

Author

Kopylov, A. P. / Problems of unique determination of domains by the relative metrics on their boundaries. In: Lobachevskii Journal of Mathematics. 2017 ; Vol. 38, No. 3. pp. 476-487.

BibTeX

@article{7d55e78ab2024687b270aabf171d178a,
title = "Problems of unique determination of domains by the relative metrics on their boundaries",
abstract = "This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique determination of domains by the relative metrics of the boundaries. Then, in Sec. 3, we study rigidity conditions for the boundaries of submanifolds in a Riemannian manifold. The final part (Sec. 4) is concernedwith the unique determination of domains by the condition of the local isometry of boundaries in the relative metrics.",
keywords = "Intrinsic metric, local isometry of boundaries, relative metric of boundary, strict convexity",
author = "Kopylov, {A. P.}",
year = "2017",
month = may,
day = "1",
doi = "10.1134/S1995080217030179",
language = "English",
volume = "38",
pages = "476--487",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "3",

}

RIS

TY - JOUR

T1 - Problems of unique determination of domains by the relative metrics on their boundaries

AU - Kopylov, A. P.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique determination of domains by the relative metrics of the boundaries. Then, in Sec. 3, we study rigidity conditions for the boundaries of submanifolds in a Riemannian manifold. The final part (Sec. 4) is concernedwith the unique determination of domains by the condition of the local isometry of boundaries in the relative metrics.

AB - This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique determination of domains by the relative metrics of the boundaries. Then, in Sec. 3, we study rigidity conditions for the boundaries of submanifolds in a Riemannian manifold. The final part (Sec. 4) is concernedwith the unique determination of domains by the condition of the local isometry of boundaries in the relative metrics.

KW - Intrinsic metric

KW - local isometry of boundaries

KW - relative metric of boundary

KW - strict convexity

UR - http://www.scopus.com/inward/record.url?scp=85019720303&partnerID=8YFLogxK

U2 - 10.1134/S1995080217030179

DO - 10.1134/S1995080217030179

M3 - Article

AN - SCOPUS:85019720303

VL - 38

SP - 476

EP - 487

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 3

ER -

ID: 10191094