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

Author： Fröhlich Steffen  

Publisher： Springer Publishing Company

ISSN： 0025-2611

Source： manuscripta mathematica, Vol.122, Iss.2, 2007-02, pp. : 149-162

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Abstract

We consider graphs with prescribed mean curvature and flat normal bundle. Using techniques of Schoen et al. (Acta Math 134:275–288, 1975) and Ecker and Huisken (Ann Inst H Poincaré Anal Non Linèaire 6:251–260, 1989), we derive the interior curvature estimate up to dimension n ≤ 5, where C is a constant depending on natural geometric data of Σ only. This generalizes previous results of Smoczyk et al. (Calc Var Partial Differ Equs 2006) and Wang (Preprint, 2004) for minimal graphs with flat normal bundle.

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