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

Abstract

We consider graphs Sigma^n 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/R^2 up to dimension n<=5, where C is a constant depending on natural geometric data of Sigma^n only. This generalizes previous results of Smoczyk, Wang and Xin, and Wang for minimal graphs with flat normal bundle.

References in corpus (1)

• On two-dimensional immersions of prescribed mean curvature in R^n

Cited by in corpus (2)

• On critical normal sections for two-dimensional immersions in R^n and a Riemann-Hilbert problem
• On critical normal sections for two-dimensional immersions in R^{n+2}