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

  • Nguyen Thi My Duyen
Keywords: Manifold with density, weighted warped product manifold, calibration

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.

Published
2020-08-10