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Some results on slices and entire graphs in certain weighted warped products

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We study the area-minimizing property of slices in the weighted warped product manifold (R+ ×f Rn, e−ϕ), assuming that the density function e−ϕ and the warping function f satisfy some additional conditions. Based on a calibration argument, a slice {t0} × Gn is proved weighted areaminimizing in the class of all entire graphs satisfying a volume balance condition and some Bernstein type theorems in R+ ×f Gn and G+ ×f Gn, when f is constant, are obtained. |

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