Maximal surfaces and graphs in a Lorentzian product -RxM

Abstract

We will present several results for maximal surfaces in a Lorentzian product manifold -R×M. The main purpose is to characterize the slices as complete maximal surfaces satisfying a comparison between the growth of lenght of the gradient of the height function and norm of the shape operator and additional bound assumptions. Several Calabi-Bernstein results are also shown. Finally, examples of maximal surfaces in -R×M are explained to emphasize the necessity of the assumptions.