### 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

## Fingerprint Dive into the research topics of 'A short proof of the minimality of Simons cone'. Together they form a unique fingerprint.

## Cite this

de Philippis, G., & Paolini, E. (2009). A short proof of the minimality of Simons cone.

*Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova*,*121*(1), 234-241. https://doi.org/10.4171/rsmup/121-14