H.V.Q. An, D.V. Cuong, N.T.M. Duyen, D.T. Hieu, T.L. Nam. On entire f-maximal graphs in the Lorentzian product Gn×R1. Journal of Geometry and Physics, 114, pp. 587–592. (2017). (ISI, IF = 0.752)

Ngày: 17/04/2017

Abstract

In the Lorentzian product Gⁿ×R₁, 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 Gⁿ×R₁ 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 Gⁿ×R₁.

Keywords

• Lorentzian product; 
• Calabi–Bernstein’s Theorem; 
• Gauss space; 
• f-maximal graphs

Link: http://doi.org/10.1016/j.geomphys.2016.12.023