On Weyl's embedding problem in Riemannian manifolds

2016/08/26 by Siyuan Lu, Lu, Siyuan · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1608.07539

openalex publication_date 2016/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a priori estimates of Weyl's embedding problem of (\mathbbS², g) in general 3-dimensional Riemannian manifold (N³, g). We establish interior C² estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of (\mathbbS²,g) in Riemannian manifold. In addition, we reprove Weyl's embedding theorem in space form under the condition that g∈ C² with D²g Dini continuous.

Citations

• Isometric embeddings into the Minkowski space and new quasi-local mass
• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• On the C 1 regularity of solutions to divergence form elliptic systems with dini-continuous coefficients

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