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

DOI10.1134/S1995080217030179zbMath1375.53072arXiv1608.04270OpenAlexW2962916461MaRDI QIDQ2399798

Anatoliĭ Pavlovich Kopylov

Publication date: 24 August 2017

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04270

zbMATH Keywords

strict convexityintrinsic metriclocal isometry of boundariesrelative metric of boundary

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Cites Work

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• A rigidity condition for the boundary of a submanifold in a Riemannian manifold
• Necessary and sufficient conditions for the unique determination of plane domains
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• Isometry of domains in \({\mathbb{R}}^ n\) and relative isometry of their boundaries
• Boundary values of mappings close to an isometric mapping
• Isometry of domains in \({\mathbb{R}}^ n\) and relative isometry of their boundaries. II
• On isometry of polygonal domains with boundaries locally isometric in relative metrics
• On unique determination of domains in Euclidean spaces
• 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

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