an:04175861
Zbl 0714.49045
Dierkes, Ulrich
On the non-existence of energy stable minimal cones
EN
Ann. Inst. Henri Poincar??, Anal. Non Lin??aire 7, No. 6, 589-601 (1990).
00156099
1990
j
49Q20
energy stable minimal cones
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.