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  "body": "\n## Summary\n\nA constant-mean-curvature surface, or CMC surface, is a surface in space whose mean curvature takes the same value at every point.\nMinimal surfaces are the case where this value is zero.\nCMC surfaces are the critical points of area among surfaces that enclose a fixed volume.\nSo they model soap bubbles and other interfaces with a pressure difference.\nRound spheres and circular cylinders are the first examples.\n\n## Explanations\n\n### L1 human\n\nA soap bubble has the same pressure difference across its wall everywhere, so its mean curvature is the same everywhere.\nThat is why a free bubble is round.\nA cylinder of radius $r$ is also a CMC surface: it bends with curvature $1/r$ around and not at all along, so the average is $1/(2r)$ at every point.\n",
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