Rendiconti del Seminario Matematico della Università di Padova


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Volume 121, 2009, pp. 233–241
DOI: 10.4171/RSMUP/121-14

A Short Proof of the Minimality of Simons Cone

Guido De Philippis[1] and Emanuele Paolini[2]

(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. Our proof 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