Uniqueness in the Local Donaldson–Scaduto Conjecture

Abstract The local Donaldson–Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi–Yau three-fold $X \times \mathbb{R}^{2}$, where $X$ is an ALE hyperkähler 4-manifold of $A_{2}$ type. The existence of this special Lagrangian has previously been proved [7]. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.