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This paper addresses the issue of uniqueness of solutions in the conformalmethod for solving the constraint equations in general relativity witharbitrary mean curvature as developed initially by Holst, Nagy, Tsogtegerel andMaxwell. We show that the solution they construct is unique amongst thosehaving volume below a certain threshold.

What Uniqueness for the Holst-Nagy-Tsogtgerel--Maxwell Solutions to the Einstein Conformal Constraint Equations?