Rendiconti del Seminario Matematico della Università di Padova
Full-Text PDF (73 KB) | Metadata | Table of Contents | RSMUP summary
Published online: 2009-06-30
A Short Proof of the Minimality of Simons ConeGuido De Philippis and Emanuele Paolini (1) SISSA, Trieste, Italy
(2) Università degli Studi di 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.
No keywords available for this article.
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