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

Authors:

Institution:

1.Technische Universit?t Darmstadt, FB Mathematik,Darmstadt,Germany;2.Centro di Ricerca Matematica Ennio De Giorgi,Scuola Normale Superiore di Pisa,Pisa,Italy

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

${\sup_{\Sigma \cap B_R} |A|^2 \leq \frac{C}{R^2}}$

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.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35J60 53A10 49Q05

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