{"paper":{"title":"A Nash-Kuiper theorem for isometric immersions in a high codimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Zhiwen Zhao","submitted_at":"2025-07-21T17:09:37Z","abstract_excerpt":"This paper is devoted to investigating the isometric immersion problem of Riemannian manifolds in a high codimension. It has recently been demonstrated that any short immersion from an $n$-dimensional smooth compact manifold into $2n$-dimensional Euclidean space can be uniformly approximated by $C^{1,\\theta}$ isometric immersions with any $\\theta\\in(0,1/(n+2))$ in dimensions $n\\geq3$. In this paper, we improve the H\\\"{o}lder regularity of the constructed isometric immersions in the local setting, achieving $C^{1,\\theta}$ for all $\\theta\\in(0,1/n)$ in odd dimensions and all $\\theta\\in(0,1/(n+1)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15808","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.15808/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}