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  "body": "\n## Summary\n\nA minimal surface is a surface in space whose mean curvature is zero at every point.\nEquivalently, small pieces of it are critical points of area: no small deformation that fixes the boundary changes the area to first order.\nSoap films spanning a wire frame are physical models of minimal surfaces.\nThe subject links differential geometry with complex analysis, the calculus of variations and partial differential equations.\n\n## Explanations\n\n### L1 human\n\nDip a wire loop into soapy water and pull it out: the film that forms tries to have as little area as possible.\nIts shape is a minimal surface.\nAt each point it bends upward in one direction exactly as much as it bends downward in the perpendicular direction, so the two bendings cancel.\nA flat disc in a flat loop is the simplest example; two parallel rings give a waisted tube called a catenoid.\n",
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