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#x2282;C2are minimal singular cones, then C1= C2This 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 #x201C;smallest#x201D; 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
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