ScalingStacks

Proposition 3.40 . [04CI]

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Proposition 3.40.

(‘special Lagrangians are minimizers’) Suppose L0L_{0} is an exact immersed special Lagrangian of phase θ^∈(−π2,π2)\hat{\theta}\in(-\frac{\pi}{2},\frac{\pi}{2}), with unobstructed bounding cochain structure. Let LL be an almost calibrated, exact, immersed Lagrangian in the same Db​F​u​k​(X)D^{b}Fuk(X) class, which intersects L0L_{0} transversely. Suppose the bordism current 𝒞\mathcal{C} with ∂𝒞=L−L0\partial\mathcal{C}=L-L_{0} satisfies automatic transversality and the positivity condition. Then 𝒮⁡(L)≥𝒮⁡(L0)\mathcal{S}(L)\geq\mathcal{S}(L_{0}).

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