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On the rigidity of constant mean curvature complete vertical graphs in warped products. (English) Zbl 1219.53056
Summary: We investigate constant mean curvature complete vertical graphs in a warped product, which is supposed to satisfy an appropriate convergence condition. In this setting, under suitable restrictions on the values of the mean curvature and the norm of the gradient of the height function, we obtain rigidity theorems concerning such graphs. Furthermore, applications to hyperbolic and Euclidean spaces are given.

53C42Immersions (differential geometry)
53C24Rigidity results (differential geometry)
Full Text: DOI
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