In 1969 Bombieri, De Giorgi and Giusti proved that Simons cone is a minimal surface, thus providing the first example of a minimal surface with a singularity. We suggest a simplified proof of the same result. Ourproof is based on the use of sub-calibrations, which are unit vector fields extending the normal vector to the surface, and having non-positive divergence. With respect to calibrations (which are divergence free) sub-calibrations are more easy to find and anyway are enough to prove the minimality of the surface.
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Guido De Philippis, Emanuele Paolini, A Short Proof of the Minimality of Simons Cone. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 233–241DOI 10.4171/RSMUP/121-14