{"paper":{"title":"The One-Sided Isometric Extension Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Micha Wasem, Norbert Hungerb\\\"uhler","submitted_at":"2014-10-01T14:12:47Z","abstract_excerpt":"Let $\\Sigma$ be a codimension one submanifold of an $n$-dimensional Riemannian manifold $M$, $n\\geqslant 2$. We give a necessary condition for an isometric immersion of $\\Sigma$ into $\\mathbb R^q$ equipped with the standard Euclidean metric, $q\\geqslant n+1$, to be locally isometrically $C^1$-extendable to $M$. Even if this condition is not met, \"one-sided\" isometric $C^1$-extensions may exist and turn out to satisfy a $C^0$-dense parametric $h$-principle in the sense of Gromov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0232","kind":"arxiv","version":4},"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"}