Generalized Thomas-Yau Uniqueness Theorems

Abstract

We generalize Thomas-Yau's uniqueness theorem in two ways. We prove a stronger statement for special Lagrangians and include minimal Lagrangians in Kähler-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.

arXiv commentMinor Changes. To appear in Birational Geometry, Kähler--Einstein Metrics and Degenerations, Springer Proceedings in Mathematics and Statistics