{"paper":{"title":"On the Unique Determination of Domains by the Condition of the Local Isometry of the Boundaries in the Relative Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Anatoly P. Kopylov","submitted_at":"2015-11-13T11:10:10Z","abstract_excerpt":"The article contains the results of the author's recent investigations of rigidity problems of domains in Euclidean spaces carried out for developing a new approach to the classical problem of the unique determination of bounded closed convex surfaces [A.V.Pogorelov, Extrinsic Geometry of Convex Surfaces, AMS, Providence (1973)], rather completely presented in [A.P.Kopylov, On the unique determination of domains in Euclidean spaces, J. of Math. Sciences, 153, no.6, 869-898 (2008)].\n  We give a complete characterization of a plane domain $U$ with smooth boundary (i.e., the Euclidean boundary $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04235","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}