Curvature estimates for minimal submanifolds of higher codimension

2007/09/24 by Y. L. Xin, Ling Yang, Xin, Y. L. +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.0709.3686

21 pages

arxiv created 2007/09/24 · openalex publication_date 2007/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken's results are generalized to higher codimension. In this way we improve Hildebrandt-Jost-Widman's result for the Bernstein type theorem.

Citations

• Curvature estimates for minimal hypersurfaces
• Minimal Varieties in Riemannian Manifolds

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