Titlebook: Lorentzian Geometry and Related Topics; GeLoMa 2016, Málaga, María A. Ca?adas-Pinedo,José Luis Flores,Francisco Conference proceedings 2017

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Constant Mean Curvature Hypersurfaces in the Steady State Space: A Survey,ifferent models of this space, we outline the major concepts, techniques, and results with a special focus on Bernstein-type theorems, hypersurfaces with boundary in a slice, and the Dirichlet problem for the constant mean curvature equation.

GRIEF

Conference proceedings 2017 status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causa

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,Calabi–Bernstein-Type Problems in Lorentzian Geometry, some of the classical and recent proofs of the theorem for the two-dimensional case, as well as several extensions for Lorentzian-warped products and other relevant spacetimes. On the other hand, the problem of uniqueness of complete maximal hypersurfaces is analyzed under the perspective of some new results.

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系列

Null Hypersurfaces on Lorentzian Manifolds and Rigging Techniques,ypersurface. We show a necessary and sufficient condition for this to happen and we give some examples. Since both rigged connection as induced connection depend on the rigging, we investigate if they can coincide for a suitable choice of the rigging.

CLAIM

Surfaces With Light-Like Points In Lorentz-Minkowski 3-Space With Applications, a surface in . whose mean curvature vector is smoothly extendable. This explains why such surfaces will contain a light-like line when they do not change causal types. Moreover, several applications of these two results are given.

Callus

2194-1009 he current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifo

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Trivalent Maximal Surfaces in Minkowski Space,ximal surfaces that are obtained by taking the real part and the imaginary part of the representation formula, and they are deformable to each other by a one-parameter family. We further introduce a compatible notion of vertex normals for general trivalent surfaces to characterize their singularities in Minkowski space as in the smooth theory.

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Space-Time Convex Functions and Sectional Curvature,vex and .-convex (.) functions, as defined by Gibbons and Ishibashi. Among the consequences are a natural construction of such functions, and an analog, that applies to domains of a new type, of a theorem of Alías, Bessa and deLira ruling out trapped submanifolds.