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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
DOI: https://doi.org/10.1090/S0002-9939-1994-1196166-6
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$.


References [Enhancements On Off] (What's this?)

  • [K] M. Kerckhove, Minimal cones and closed differential forms on $ {\text{SO}}(n) \times {\Lambda _n}$, preprint.
  • [L] G. Lawlor, A sufficient criterion for a cone to be area-minimizing, Mem. Amer. Math. Soc., vol. 91, no. 446, Amer. Math. Soc., Providence, RI, 1991. MR 1073951 (92d:49079)
  • [Mh1] T. Murdoch, Twisted calibrations, Trans. Amer. Math. Soc. 328 (1991), 239-257. MR 1069738 (92c:53042)
  • [Mh2] -, Calibrations arising from the adjoint action of $ {\text{SO}}(n)$, preprint.

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Additional Information

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

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