Future complete Einsteinian space times with U(1) symmetry, the unpolarized case

Abstract

I prove the existence of vacuum S1 symmetric Einsteinian, unpolarized, space times which are complete in the direction of the expansion, for small initial data, without supposing that the S1 orbits are orthogonal to the 3-manifolds, as was done in previous work in collaboration with V. Moncrief.

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