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

Результат исследования: Научные публикации в периодических изданияхстатья

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)986-993
Число страниц8
ЖурналSiberian Electronic Mathematical Reports
Том14
DOI
СостояниеОпубликовано - 1 янв 2017

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