Rendiconti del Seminario Matematico della Università di Padova
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A Short Proof of the Minimality of Simons ConeGuido De Philippis and Emanuele Paolini (1) SISSA, Via Bonomea 265, 34136, Trieste, Italy
(2) Dipartimento Matematica 'U.Dini', Università degli Studi di Firenze, Viale Morgagni, 67/a, 50134, Firenze, Italy
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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De Philippis Guido, Paolini Emanuele: A Short Proof of the Minimality of Simons Cone. Rend. Sem. Mat. Univ. Padova 121 (2009), 233-241. doi: 10.4171/RSMUP/121-14