Email this article Problems of unique determination of domains by the relative metrics on their boundaries
- Authors: Kopylov A.P.1,2
-
Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 38, No 3 (2017)
- Pages: 476-487
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199274
- DOI: https://doi.org/10.1134/S1995080217030179
- ID: 199274
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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.
About the authors
A. P. Kopylov
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: apkopylov@yahoo.com
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
