Generalized Thomas-Yau Uniqueness Theorems

TL;DR

This paper extends the Thomas-Yau uniqueness theorem to include minimal Lagrangians in Kähler-Einstein manifolds and J-minimal Lagrangians, employing Hamiltonian perturbations and advanced methods.

Contribution

It provides a generalized and stronger uniqueness theorem for special Lagrangians, incorporating minimal and J-minimal cases with new proof techniques.

Findings

Proved a stronger uniqueness theorem for special Lagrangians.

Included minimal Lagrangians in Kähler-Einstein manifolds.

Utilized Hamiltonian perturbations and methods by Imagi, Joyce, and Oliveira dos Santos.

Abstract

We generalize Thomas-Yau's uniqueness theorem in two ways. We prove a stronger statement for special Lagrangians and include minimal Lagrangians in K\"ahler-Einstein manifold or more generally J-minimal Lagrangians introduced by Lotay and Pacini. In every case the heart of the proof is to make certain Hamiltonian perturbations. For this we use the method by Imagi, Joyce and Oliveira dos Santos.