Power Mean Curvature Flow in Lorentzian Manifolds

Details Power Mean Curvature Flow in Lorentzian Manifolds Power Mean Curvature Flow in Lorentzian Manifolds

2006-02-13

arxiv.org/abs/math/0602268v1

Mathematics

Differential Geometry

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Scientific paper

We study the motion of an $n$-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power $p$ of the mean curvature. We prove that for any $p\in (0,1]$, the flow exists for all time when the Ricci tensor of the ambient space is bounded from below on the set of timelike unit vectors. Moreover, if we assume that all envolving hypersurfaces stay in a precompact region, then the flow converges to a stationary maximum spacelike hypersurface.

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