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

In this article, we give nonexistence and nonuniqueness results for the vacuum Einstein conformal constraint equations in the far from CMC case and also show that in some cases the equations of the conformal method for positive Yamabe metrics and with TT-tensor $\sigma \equiv 0$ have a non-trivial solution, and thus answer a question by D. Maxwell.

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Received 3 November 2015

Published 3 January 2019