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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)476-487
Number of pages12
JournalLobachevskii Journal of Mathematics
Volume38
Issue number3
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Intrinsic metric
  • local isometry of boundaries
  • relative metric of boundary
  • strict convexity

Fingerprint Dive into the research topics of 'Problems of unique determination of domains by the relative metrics on their boundaries'. Together they form a unique fingerprint.

Cite this