A short proof of the minimality of Simons cone. (English) Zbl 1165.53305
E. Bombieri, E. de Giorgi, and E. Giusti [Invent. Math., 243–268 (1969; Zbl 0183.25901)] proved that the 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.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
Citations:
Zbl 0183.25901References:
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