Uniqueness and persistence of minimal Lagrangian submanifolds

Jason D. Lotay, Tommaso Pacini

Published 2017-04-26Version 1

We prove that, in a negative K\"ahler--Einstein manifold M, compact minimal Lagrangian submanifolds L are locally unique and for any small K\"ahler--Einstein perturbation of M there corresponds a deformation of L which is minimal Lagrangian with respect to the new structure. This provides a new source of examples of minimal Lagrangians. Our results are a simple application of the J-volume functional discussed in arXiv:1404.4227, arXiv:1506.04630