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We present a proof of the Riemannian Penrose inequality with charge in thecontext of asymptotically flat initial data sets for the Einstein-Maxwellequations, having possibly multiple black holes with no charged matter outsidethe horizon, and satisfying the relevant dominant energy condition. The proofis based on a generalization of Hubert Bray's conformal flow of metrics adaptedto this setting.

Proof of the Riemannian Penrose Inequality with Charge for Multiple Black Holes