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.
A short proof of the minimality of Simons cone / De Philippis, G; Paolini, E. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 121:1(2009), pp. 233-241. [10.4171/RSMUP/121-14]
A short proof of the minimality of Simons cone
De Philippis, G;
2009-01-01
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.| File | Dimensione | Formato | |
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