Power Mean Curvature Flow in Lorentzian Manifolds

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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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Differential Geometry, General Relativity and Quantum Cosmology, Analysis of PDEs, Primary: 53C44, 53C21; Secondary: 58J35, 83E99

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http://salesiana.dossiersoluciones.com/handle/123456789/108945

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602268
 http://arxiv.org/abs/math/0602268

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arXiv