The object of study are complete spacelike hypersurfaces in a generalized Robertson-Walker spacetime. We make use of a new local form of the weak maximum principle for a class of operators including the Lorentzian mean curvature operator in order to obtain some mean curvature estimates and height estimates for spacelike hypersurfaces. These estimates are related to some rigidity results. We also give height estimates for spacelike hypersurfaces with constant higher order mean curvature, which are obtained via the local form of the weak maximum principle for an appropriate class of operators.
SPACELIKE HYPERSURFACES IN GENERALIZED ROBERTSON-WALKER SPACETIMES / S. Scoleri ; Advisor: M. Rigoli ; coordinator: L. Van Geemen. Università degli Studi di Milano, 2014 Dec 04. 26. ciclo, Anno Accademico 2013. [10.13130/scoleri-simona_phd2014-12-04].
SPACELIKE HYPERSURFACES IN GENERALIZED ROBERTSON-WALKER SPACETIMES
S. Scoleri
2014
Abstract
The object of study are complete spacelike hypersurfaces in a generalized Robertson-Walker spacetime. We make use of a new local form of the weak maximum principle for a class of operators including the Lorentzian mean curvature operator in order to obtain some mean curvature estimates and height estimates for spacelike hypersurfaces. These estimates are related to some rigidity results. We also give height estimates for spacelike hypersurfaces with constant higher order mean curvature, which are obtained via the local form of the weak maximum principle for an appropriate class of operators.
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