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  "body": "\n## Example\n\nCosta's surface is a complete [[minimal surface|41X0YW2R9N]] in $\\R^3$ that is embedded and has finite total curvature.\nTopologically it is a torus with three points removed.\nNear the three removed points the surface has three ends: two look like the ends of a [[catenoid|6NN1HP54GB]] and one looks like a plane.\n\nIt is built with the [[Weierstrass–Enneper parameterization|YWV6J23AP6]].\nThe domain is the square torus $\\C / (\\Z + i\\Z)$ minus three points, and the data are given by the Weierstrass $\\wp$ function of this lattice.\nOne checks that the real periods of the integrals vanish, so the surface is well defined, and minimality then follows from the parameterization.\nThe hard part, proved later, is that the surface has no self-intersections.\n\n## Remarks\n\nCosta described the surface in 1982, and Hoffman and Meeks proved that it is embedded.\nBefore it, the only known complete embedded minimal surfaces of finite topology were the plane, the catenoid and the helicoid.\nIts total curvature is $-12\\pi$.\n\n## Explanations\n\n### L1 human\n\nCosta's surface looks like a catenoid with a flat sheet slicing through its waist, where the sheet and the tube are joined by two tunnels instead of crossing.\nIt has a hole like a doughnut and goes off to infinity in three directions.\nIts discovery showed that minimal surfaces without self-crossings are much more varied than had been thought.\n",
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