This article is cited in 5 scientific papers (total in 5 papers)
A criterion for the unique determination of domains in Euclidean spaces by the metrics of their boundaries induced by the intrinsic metrics of the domains
M. V. Korobkovab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
We say that a domain $U\subset\mathbb R^n$ is uniquely determined by the relative metric (which is the extension by continuity of the intrinsic metric of the domain on its boundary) of its Hausdorff boundary if any domain $V\subset\mathbb R^n$ such that its Hausdorff boundary is isometric in the relative metric to the Hausdorff boundary of $U$, is isometric to $U$ in the Euclidean metric. In this paper, we obtain the necessary and sufficient conditions for the uniqueness of determination of a domain by the relative metric of its Hausdorff boundary.
domain, Hausdorff limit, relative metric, intrinsic metric, uniqueness of determination.
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Siberian Advances in Mathematics, 2010, 20:4, 256–284
M. V. Korobkov, “A criterion for the unique determination of domains in Euclidean spaces by the metrics of their boundaries induced by the intrinsic metrics of the domains”, Mat. Tr., 12:2 (2009), 52–96; Siberian Adv. Math., 20:4 (2010), 256–284
Citation in format AMSBIB
\paper A criterion for the unique determination of domains in Euclidean spaces by the metrics of their boundaries induced by the intrinsic metrics of the domains
\jour Mat. Tr.
\jour Siberian Adv. Math.
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A. P. Kopylov, “On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics”, Sib. elektron. matem. izv., 14 (2017), 59–72
A. P. Kopylov, “On the unique determination of domains by the condition of the local isometry of the boundaries in the relative metrics. II”, Sib. elektron. matem. izv., 14 (2017), 986–993
Kopylov A.P., “Problems of Unique Determination of Domains By the Relative Metrics on Their Boundaries”, Lobachevskii J. Math., 38:3, SI (2017), 476–487
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