Complex analytic properties of minimal Lagrangian submanifolds

In this article we study complex properties of minimal Lagrangian submanifolds in Kähler ambient spaces, and how they depend on the ambient curvature. In particular, we prove that, in the negative curvature case, minimal Lagrangians do not admit fillings by holomorphic discs. The proof relies on a mix of holomorphic curve techniques and on recent convexity results for a perturbed volume functional.

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Received 14 August 2018

Accepted 28 May 2019

Published 28 October 2020