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

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

2006-03-28

arxiv.org/abs/math/0603659v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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