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The converse is impossible in any context where the isoperimetric inequality is applicable.
by Chinjut 10y ago
The converse is impossible in any context where the isoperimetric inequality is applicable.
- tgb 10y agoGood point. Though the Wikipedia article on it gives the most general form as requiring our region to have closure with finite Lebesgue measure. This is necessary of course by the example another corner brought up about swapping the inside and outside. But that means it exactly can't rule out the existence of regions with infinite volume (outside and inside) and finite surface area!