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European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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121
2009
0
A Short Proof of the Minimality of Simons Cone
Guido
De Philippis
Universität Zürich, ZÜRICH, SWITZERLAND
Emanuele
Paolini
Università degli Studi di Firenze, 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.
General
233
241
10.4171/RSMUP/121-14
http://www.ems-ph.org/doi/10.4171/RSMUP/121-14