Volume preserving curvature flows in Lorentzian manifolds

Matthias Makowski

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arXiv · 1104.2213

Volume preserving curvature flows in Lorentzian manifolds

Matthias Makowski

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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 $C^\infty$-topology to a hypersurface of constant F-curvature. Furthermore we examine stability properties and foliations of constant F-curvature hypersurfaces.

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Matthias Makowski. 2011-04-12. Volume preserving curvature flows in Lorentzian manifolds. https://arxiv.org/abs/1104.2213

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