Volume preserving curvature flows in Lorentzian manifolds

2011/04/12 by Matthias Makowski, Makowski, Matthias
Mathematics · #35K55 #35K93 #53C44 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35K55 #msc:35K93 #msc:53C44 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1104.2213

43 pages

arxiv created 2011/04/12 · arxiv updated 2011/04/13

Abstract

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^∞-topology to a hypersurface of constant F-curvature. Furthermore we examine stability properties and foliations of constant F-curvature hypersurfaces.

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