Proof of the closed-universe recollapse conjecture for general bianchi type-IX cosmologies

It is proven that there do not exist any Bianchi type-IX universes which expand for an infinite time, provided only that the matter satisfies the dominant energy condition and has non-negative average pressure (i.e., a non-negative trace of the spatial projection of the stress-energy tensor). This generalizes a proof recently given by us for the case of diagonal Bianchi type-IX solutions.