Uniqueness of complete maximal surfaces in a Lorentzian Product \(-\mathbb{R}\times M\)
Eraldo Almeida Lima Junior Universidade Federal do Ceará, Centro de Ciências e Tecnologia
We will present several results for maximal surfaces in a Lorentzian product manifold \(-\mathbb{R}\times M\). 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 \(-\mathbb{R}\times M\) are explained to emphasize the necessity of the assumptions.