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 3-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. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.

Final version, published in International Mathematics Research Notices, 19 pages