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.
Sharp lower bound for the charged Hawking mass in the electrostatic space
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abstract
We prove sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times in various contexts. An upper bound for the genus of stable surfaces in the electrostatic system is provided. We also study the positivity for the charged Hawking mass of a minimal surface with index one in the electrostatic space-times. A criterion for a CMC surface in the Reissner-Nordstrom deSitter space to be stable is presented.
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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.