# From minimal Lagrangian to J-minimal submanifolds: persistence and uniqueness

## TL;DR

This paper demonstrates that minimal Lagrangian and J-minimal submanifolds in negatively curved Kähler-Einstein manifolds persist under small perturbations, providing new examples and insights into their stability and uniqueness.

## Contribution

It establishes the persistence and uniqueness of minimal Lagrangian and J-minimal submanifolds under small perturbations of the ambient Kähler structure.

## Key findings

- Minimal Lagrangian submanifolds persist under small Kähler-Einstein perturbations.
- J-minimal submanifolds in negatively curved Kähler manifolds also persist.
- Provides new examples of minimal Lagrangian submanifolds in perturbed structures.

## Abstract

Given a minimal Lagrangian submanifold L in a negative Kaehler--Einstein manifold M, we show that any small Kaehler--Einstein perturbation of M induces a deformation of L which is minimal Lagrangian with respect to the new structure. This provides a new source of examples of minimal Lagrangians. More generally, the same is true for the larger class of totally real J-minimal submanifolds in Kaehler manifolds with negative definite Ricci curvature.