2006/02/13 by Guanghan Li, Li, Guanghan, Isabel M. C. Salavessa +1
Mathematics · Physics and Astronomy · #53C21 #83E99 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 53C44 #Secondary: 58J35 #gr-qc #math.AP #math.DG #msc:53C21 #msc:53C44 #msc:58J35 #msc:83E99
paper · pdf · doi:10.48550/arxiv.math/0602268
Latex
arxiv created 2006/02/13 · openalex publication_date 2006/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∈ (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.