A Short Proof of the Minimality of Simons Cone
Guido De Philippis
SISSA, Trieste, ItalyEmanuele Paolini
Università degli Studi di Firenze, Italy
Abstract
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.
Cite this article
Guido De Philippis, Emanuele Paolini, A Short Proof of the Minimality of Simons Cone. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 233–241
DOI 10.4171/RSMUP/121-14