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Oct 25, 2022 at 19:32 comment added Didier @RBega2 You are aright. I edited my answer.
Oct 25, 2022 at 19:31 history edited Didier CC BY-SA 4.0
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Oct 25, 2022 at 17:26 comment added RBega2 While your reference is very interesting I don't think it shows the isoperimetric inequality rather it shows that if the least area set containing a given volume had sufficiently large Hermitian mean curvature, then it would have to be a ball -- it can't rule out exotic examples that are more efficient for area but have smaller Hermitian mean curvature. Theorem E shows the result if the minimizer is Hopf.
Oct 25, 2022 at 14:39 history answered Didier CC BY-SA 4.0