Titlebook: Recent Trends in Lorentzian Geometry; Miguel Sánchez,MIguel Ortega,Alfonso Romero Conference proceedings 2013 Springer Science+Business Me

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Conference proceedings 2013haviors, far from classical Riemannian techniques. Recent progress has attracted a renewed interest in this theory for many researchers: long-standing global open problems have been solved, outstanding Lorentzian spaces and groups have been classified, new applications to mathematical relativity and

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Area Inequalities for Stable Marginally Trapped Surfaces,vide lower bounds for the area of spatial sections of dynamical trapping horizons, namely hypersurfaces offering quasi-local models of black hole horizons. In particular, these inequalities represent particular examples of the extension to a Lorentzian setting of tools employed in the discussion of minimal surfaces in Riemannian contexts.

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2194-1009 odesics, submanifolds, causality, black holes, geometry of s.Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques. Recent progress has attracted a renewed

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Umbilical-Type Surfaces in SpaceTime,amental form along . is proportional to the first fundamental form of .. In particular, . is pseudo-umbilical if it is umbilical along the mean curvature vector field . and (totally) umbilical if it is umbilical along all possible normal directions. The possibility that the surface be umbilical alon

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Area Inequalities for Stable Marginally Trapped Surfaces,cuum dynamical spacetimes, with non-negative cosmological constant and matter sources satisfying the dominant energy condition. These inequalities provide lower bounds for the area of spatial sections of dynamical trapping horizons, namely hypersurfaces offering quasi-local models of black hole hori

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