Abstract
We consider graphs \({{\Sigma^n \subset \mathbb{R}^m}}\) 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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Fröhlich, S., Winklmann, S. Curvature estimates for graphs with prescribed mean curvature and flat normal bundle. manuscripta math. 122, 149–162 (2007). https://doi.org/10.1007/s00229-006-0060-4
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DOI: https://doi.org/10.1007/s00229-006-0060-4