Thomas-Yau's special-Lagrangian minimizer conjecture

Let $\mathcal{L}$ be the admissible class of Lagrangian objects and let $\mathcal{S}$ be the Solomon functional. A special Lagrangian is a Lagrangian on which the relevant holomorphic volume form has constant phase. Thomas-Yau's minimizer conjecture. If there exists a special Lagrangian $L\in\mathcal{L}$ in the relevant class, then $L$ is a minimizer of the Solomon functional. The source presents this as a conjectural extension of an earlier result beyond automatic transversality, positivity, and smoothness assumptions; it is intended to show that special Lagrangians minimize the variational functional.