Curvature estimates for graphs with prescribed mean curvature and flat normal bundle

2006/03/28 by Steffen Froehlich, Froehlich, Steffen, Sven Winklmann +1
Mathematics · Physics and Astronomy · #35J60 #49Q05 #53A10 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:35J60 #msc:49Q05 #msc:53A10

paper · pdf · doi:10.48550/arxiv.math/0603659

arxiv created 2006/03/28 · openalex publication_date 2006/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider graphs Sigmaⁿ in R^m with prescribed mean curvature and flat normal bundle. Using techniques of Schoen, Simon and Yau, and Ecker-Huisken, we derive an interior curvature estimate of the form |A|²<=C/R² up to dimension n<=5, where C is a constant depending on natural geometric data of Sigmaⁿ only. This generalizes previous results of Smoczyk, Wang and Xin, and Wang for minimal graphs with flat normal bundle.

Citations

• Curvature estimates for minimal hypersurfaces
• Minimal Varieties in Riemannian Manifolds
• On two-dimensional immersions of prescribed mean curvature in Rⁿ

Related

• On 2-surfaces in R⁴ and Rⁿ
• Curvature estimates for submanifolds with prescribed Gauss image and mean curvature
• On a sharp form of curvature conjecture for minimal graphs
• Stability and curvature estimates for minimal graphs with flat normal bundles
• Height estimates for constant mean curvature graphs in Nil₃ and \widetildePSL₂(ℝ)