On minimal cones

Abstract

This paper contains tow new results about minimal sets in euclidean spaces. The first one, see Theorem 2.4, is of the Maximum principle type, and proves that if C₁⊂C₂ are minimal singular cones, then C₁= C₂ This result completes those proven in16 and 17. The second result, see Theorem 3.1, proves that in every singular minimal cone , a nonempty minimal set E is strictly contained. If C is the “smallest” singular minimal cone in its dimension, see Theorem 3.2, then the boundary of E is analytic, see Remark 3.3. A similar result was proven in [18]

Keywords:

• geometric measure theory
• minimal sets minimal cones
• Bernstein problem