Abstract
We extend the technique developed by S.T. Yau in [21] in order to investigate the rigidity of entire vertical graphs in a Riemannian product space ℝ × Mn, whose fiber Mn is supposed to have Ricci curvature with strict sign. In this setting, under a suitable restriction on the norm of the gradient of the function u which determines such a graph Σn (u), we are able to prove that Σn (u) must be a slice {t} × Mn.
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