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- W2095060311 abstract "Let G be a compact semisimple Lie group, g its Lie algebra, (,) an AdG-invariant inner product on g, and M an adjoint orbit in 9. In this article, if (M,(,)|M) is Kähler with respect to its canonical complex structure, then we give, for a closed minimal Lagrangian submanifold L⊂M, upper bounds on the first positive eigenvalue λ1(L) of the Laplacian ΔL, which acts on C∞(L), and lower bounds on the volume of L. In particular, when (M,(,)|M) is Kähler-Einstein, (p=cω, where p and ω are Ricci form and Kähler form of (M,(,)|M) with respect to the canonical complex structure respectively, and c is a positive constant,) we prove λ1(L)≤c. Combining with a result of Oh [5], we can see that L is Hamiltonian stable if and only if λ1(L)=c." @default.
- W2095060311 created "2016-06-24" @default.
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- W2095060311 date "2003-01-01" @default.
- W2095060311 modified "2023-09-25" @default.
- W2095060311 title "Minimal Lagrangian submanifolds in adjoint orbits and upper bounds on the first eigenvalue of the Laplacian" @default.
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- W2095060311 doi "https://doi.org/10.2969/jmsj/1196890852" @default.
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