Symplectic embeddings into cylinders for certain symplectic manifolds

Year 2025, Volume: 54 Issue: 6, 2322 - 2325, 30.12.2025

Nil Ipek Sirikci

https://doi.org/10.15672/hujms.1451185

Abstract

We present a proof of a result on displaceability of subsets of symplectic manifolds satisfying certain conditions one of which is that the subset is precompact in a connected neighborhood that symplectically embeds into $\mathbb{R}^{2n}$. The proof utilizes an inequality between the displacement energy and the cylindrical capacity for subsets of $\mathbb{R}^{2n}$ to obtain an inequality for subsets of the symplectic manifold. We also state a corollary which utilizes other results on nondisplaceable Lagrangians.

Keywords

symplectic embeddings , symplectic manifolds , Lagrangian submanifolds , symplectic cylinder , displacement energy , cylindrical capacity

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