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Proceedings of the American Mathematical Society

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Isolated orbits of the adjoint action and area-minimizing cones


Author: Michael Kerckhove
Journal: Proc. Amer. Math. Soc. 121 (1994), 497-503
MSC: Primary 49Q05; Secondary 53C42
MathSciNet review: 1196166
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Abstract: Using a criterion of Lawlor, it is shown that the cone over an isolated orbit of the adjoint action of $ {\text{SU}}(n)$ on the unit sphere in the vector space of traceless n-by- n Hermitian symmetric matrices is area-minimizing for $ n > 2$. Likewise, the cone over an isolated orbit of the adjoint action of $ {\text{SO}}(n)$ is shown to be area-minimizing for $ n > 3$.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1196166-6
Keywords: Area-minimizing surface, cone
Article copyright: © Copyright 1994 American Mathematical Society