Isolated orbits of the adjoint action and area-minimizing cones
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- by Michael Kerckhove PDF
- Proc. Amer. Math. Soc. 121 (1994), 497-503 Request permission
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
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M. Kerckhove, Minimal cones and closed differential forms on ${\text {SO}}(n) \times {\Lambda _n}$, preprint.
- Gary R. Lawlor, A sufficient criterion for a cone to be area-minimizing, Mem. Amer. Math. Soc. 91 (1991), no. 446, vi+111. MR 1073951, DOI 10.1090/memo/0446
- Timothy A. Murdoch, Twisted calibrations, Trans. Amer. Math. Soc. 328 (1991), no. 1, 239–257. MR 1069738, DOI 10.1090/S0002-9947-1991-1069738-9 —, Calibrations arising from the adjoint action of ${\text {SO}}(n)$, preprint.
Additional Information
- © Copyright 1994 American Mathematical Society
- 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