Volume preserving curvature flows in Lorentzian manifolds

Details Volume preserving curvature flows in Lorentzian manifolds Volume preserving curvature flows in Lorentzian manifolds

2011-04-12

arxiv.org/abs/1104.2213v1

Mathematics

Differential Geometry

43 pages

Scientific paper

Let N be a (n+1)-dimensional globally hyperbolic Lorentzian manifold with a compact Cauchy hypersurface. We consider curvature flows in N with different curvature functions F (including the mean curvature, the gauss curvature and the second elementary symmetric polynomial) and a volume preserving term. Under suitable assumptions we prove the long time existence of the flow and the exponential convergence of the corresponding graphs in the $C^\infty$-topology to a hypersurface of constant F-curvature. Furthermore we examine stability properties and foliations of constant F-curvature hypersurfaces.

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