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In this article, we give nonexistence and nonuniqueness re ults for the vacuum Einstein conformal constraint equations in the far from CMC case and a lso show that in some cases the equations of the conformal method for positive Yamabe metrics and with TT-tensorσ ≡ 0 have a non-trivial solution, and thus answer a question by D. Maxwell [ 18].

Nonexistence and nonuniqueness results for solutions to the vacuum Einstein conformal constraint equations