Uniqueness in the local Donaldson-Scaduto conjecture

TL;DR

This paper proves the uniqueness of a special Lagrangian pair of pants predicted by the local Donaldson-Scaduto conjecture in a specific Calabi-Yau setting, confirming that no other such solutions exist.

Contribution

It establishes a uniqueness theorem for the special Lagrangian pair of pants in the context of the local Donaldson-Scaduto conjecture, complementing previous existence results.

Findings

Proves the uniqueness of the special Lagrangian pair of pants.

Confirms the conjecture's prediction of a unique solution.

Strengthens understanding of special Lagrangians in Calabi-Yau manifolds.

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 hyperk\"ahler 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.