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{Volume preserving curvature flows in Lorentzian manifolds}

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We consider volume preserving curvature flows in globally hyperbolic Lorentzian manifolds with a compact Cauchy hypersurface. Possible choices of curvature functions F include the mean curvature, the square root of the second elementary symmetric polynomial as well as the n-th root of the Gaussian curvature. Under the assumption of barriers and some curvature assumptions on the ambient manifold we prove long time existence of the flow and exponential convergence to a hypersurface of constant F-curvature. Furthermore we examine stability properties and foliations of the ambient manifold by constant F-curvature hypersurfaces.

This paper has appeared in "Calc. Var. and Partial Differential Equations". Springer-Verlag is the copyright holder of this article. The original publication is available on http://www.springerlink.com/content/41624268468x07h3/.