Abstract
ABSTRACTWe prove future nonlinear stability of homogeneous solutions to the Einstein–Vlasov system with massive particles on manifolds with topology M = ℝ×Σ, where Σ is either 𝕊2 or 𝕋2. For the sphere this implies the existence of an open subset of the initial data manifold with elements of strictly positive scalar curvature, whose developments are future geodesically complete. In combination with an earlier result for hyperbolic surfaces we conclude future completeness for the Einstein–Vlasov system in 2+1 dimensions independent of the compact spatial topology for an open set of initial data.
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