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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 3, Pages 548–567
(Mi smj1861)
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This article is cited in 4 scientific papers (total in 4 papers)
Necessary and sufficient conditions for unique determination of plane domains
M. V. Korobkov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We say that a domain $U\in\mathbb R^n$ is uniquely determined from the relative metric of its Hausdorff boundary (the relative metric is the extension by continuity of the intrinsic metric of the domain to the boundary) if every domain $V\in\mathbb R^n$ with the Hausdorff boundary isometric in the relative metric to the Hausdorff boundary of $U$ is isometric to $U$ too (in the Euclidean metrics). In this article we state some necessary and sufficient conditions for a plane domain to be uniquely determined from the relative metric of its Hausdorff boundary.
Keywords:
plane domain, Hausdorff boundary, relative metric, unique determination.
Received: 15.08.2006
Citation:
M. V. Korobkov, “Necessary and sufficient conditions for unique determination of plane domains”, Sibirsk. Mat. Zh., 49:3 (2008), 548–567; Siberian Math. J., 49:3 (2008), 436–451
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https://www.mathnet.ru/eng/smj1861 https://www.mathnet.ru/eng/smj/v49/i3/p548
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Abstract page: | 271 | Full-text PDF : | 71 | References: | 38 |
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