Symplectic embeddings of polydisks

Symplectic folding and non-isotopic polydisks

Our main result demonstrates the existence of different Hamiltonian isotopy classes of symplectically embedded polydisks inside a 4-ball, and by the same argument also in the complex projective plane. Furthermore, we find exactly how large the ball can be before the embeddings become isotopic; the optimal isotopy is a version of symplectic folding. Before stating the result precisely we fix som...

On Holomorphic Isometric Embeddings of the Unit Disk into Polydisks

We study the classification of holomorphic isometric embeddings of the unit disk into polydisks. As a corollary of our results, we can give a complete classification when the target is the 2-disk and the 3-disk. We also prove that the holomorphic isometric embeddings between polydisks are induced by those of the unit disk into polydisks.

Embeddings of polydisks

An Extension Theorem in Symplectic Geometry

We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

Symplectic Hypersurfaces in C

We establish the uniqueness of the symplectic 4-manifolds which admit low degree symplectic embeddings into CP 3. We also discuss the uniqueness of the fundamental group of the complement of such embeddings into arbitrary symplectic 6-manifolds. 2000 Mathematics Subject Classification: Primary 57R17; Secondary 57R95.