Abstract
In the Lorentzian product G n × R 1 , we give a comparison theorem between the f -volume of an entire f -maximal graph and the f -volume of the hyperbolic H r + under the condition that the gradient of the function defining the graph is bounded away from 1. This condition comes from an example of non-planar entire f -maximal graph in G n × R 1 and is equivalent to the hyperbolic angle function of the graph being bounded. As a consequence, we obtain a Calabi–Bernstein type theorem for f -maximal graphs in G n × R 1 .
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