Punctured holomorphic curves and Lagrangian embeddings

By Kai Cieliebak, Klaus Mohnke. 2014

94 citations recorded by the source corpus.

We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin’s conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold’s chord conjecture, and estimates on the size of Weinstein neighbourhoods. The main technical ingredient is transversality for the relevant moduli spaces of punctured holomorphic curves with tangency conditions.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57e250d5192ab82ea2ec54ce75d56b643a299a92

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Symplectic capacities from positive S1–equivariant symplectic homology (2017, background): “This is related to the following question of Cieliebak-Mohnke [CM14].”