A short proof of the minimality of Simons cone

G. de Philippis, E. Paolini

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)234-241
Number of pages8
JournalRendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume121
Issue number1
DOIs
StatePublished - 2009

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology

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