SOME RESULTS ON SLICES AND ENTIRE GRAPHS IN CERTAIN WEIGHTED WARPED PRODUCTS

Abstract

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.