{"paper":{"title":"On Weyl's embedding problem in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Siyuan Lu","submitted_at":"2016-08-26T17:54:32Z","abstract_excerpt":"We consider a priori estimates of Weyl's embedding problem of $(\\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \\bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of $(\\mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's embedding theorem in space form under the condition that $g\\in C^2$ with $D^2g$ Dini continuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07539","kind":"arxiv","version":2},"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"}