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We study isoperimetric surfaces in the Reissner-Nordstr\"om spacetime, withemphasis on the cuasilocal inequality between area and charge. We analyze thestability of the isoperimetric spheres and we found that there is a lower boundon the area in terms of the charge, and that the inequality is saturated in thetransition from the superextremal to the subextremal case. We also derive ageneral inequality between area and charge for stable isoperimetric surfaces inmaximal electro-vacuum initial data.

Stable isoperimetric surfaces in super-extreme Reissner-Nordstr\"om