On area-constrained critical surfaces of the Hawking functional, zero Hawking energy implies the enclosed region is flat or the reference space form, but the dynamical statement is conditional on a restrictive technical assumption.
Bray,On the positive mass, penrose, an zas inequalities in general dimension, surveys in geo- metric analysis and relativity, adv
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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces
On area-constrained critical surfaces of the Hawking functional, zero Hawking energy implies the enclosed region is flat or the reference space form, but the dynamical statement is conditional on a restrictive technical assumption.