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Complex analytic properties of minimal Lagrangian submanifolds. (English) Zbl 1475.53070

Summary: 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.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53D12 Lagrangian submanifolds; Maslov index
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q20 Kähler-Einstein manifolds
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