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On the non-existence of energy stable minimal cones. (English) Zbl 0714.49045
Summary: We show that there are no non-trivial (potential) energy stable minimal cones in \({\mathbb{R}}^ n\times {\mathbb{R}}^+\) with singularity at 0, if \(2\leq n\leq 5\). The sharpness of this result is demonstrated by proving that a certain six dimensional cone in \({\mathbb{R}}^ 7\) is stable. Moreover, we extend all results to the more general \(\alpha\)-energy functional.

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
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