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# 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.

seminario 1ª Planta, IEMath-GR

# Calabi-Bernstein results in Lorentzian product spaces

## Eraldo Almeida Lima Junior Universidade Federal do Ceará, Centro de Ciências e Tecnologia

We deal with two-sided complete hypersurfaces immersed in a Lorentzian product space, whose base is supposed to have sectional curvature bounded from below. In this setting, we obtain suffi cient conditions which assure that such a spacelike hypersurface is a slice of the ambient space, provided that its angle function has some suitable behavior. Furthermore, we establish a natural relation between our results and the classical problem of to describe the geometry of a hypersurface immersed in the Euclidean space through the behavior of its Gauss map.

seminario 1ª Planta, IEMath-Gr

# Eraldo Almeida Lima Junior

## Universidade Federal do Ceará, Centro de Ciências e Tecnologia

Number of talks
2
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Brasil