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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 234-241 |
| Number of pages | 8 |
| Journal | Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova |
| Volume | 121 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2009 |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Mathematical Physics
- Geometry and Topology