On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)986-993
Number of pages8
JournalСибирские электронные математические известия
Volume14
DOIs
Publication statusPublished - 1 Jan 2017

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

OECD FOS+WOS

  • 1.01 MATHEMATICS

Fingerprint Dive into the research topics of 'On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II'. Together they form a unique fingerprint.

Cite this