$J$-holomorphic cylinders between ellipsoids in dimension four

@article{Hind2017JholomorphicCB,
  title={\$J\$-holomorphic cylinders between ellipsoids in dimension four},
  author={Richard Hind and Ely Kerman},
  journal={arXiv: Symplectic Geometry},
  year={2017}
}
We establish results concerning the existence and nonexistence of regular $J$-holomorphic cylinders between nested pairs of ellipsoids in $\mathbb{R}^4$. 
3 Citations
A remark on the stabilized symplectic embedding problem for ellipsoids
This note constructs sharp obstructions for stabilized symplectic embeddings of an ellipsoid into a ball, in the case when the initial four-dimensional ellipsoid has ‘eccentricity’ of the form
Symplectic capacities, unperturbed curves, and convex toric domains
We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second named author using
Correction To: New obstructions to symplectic embeddings
We correct here an error in the proof of Theorem 1.1 of our paper “New obstructions to symplectic embeddings,” henceforth referred to as [6].

References

SHOWING 1-10 OF 12 REFERENCES
A remark on the stabilized symplectic embedding problem for ellipsoids
This note constructs sharp obstructions for stabilized symplectic embeddings of an ellipsoid into a ball, in the case when the initial four-dimensional ellipsoid has ‘eccentricity’ of the form
Symplectic embeddings of products
McDuff and Schlenk determined when a four-dimensional ellipsoid can be symplectically embedded into a four-dimensional ball, and found that when the ellipsoid is close to round, the answer is given
Maximal symplectic packings in ${\mathbb {P}^2}$
Abstract In this paper we describe the intersections between the balls of maximal symplectic packings of $\mathbb {P}^2$. This analysis shows the existence of singular points for maximal packings of
Contact homology and virtual fundamental cycles
  • J. Pardon
  • Mathematics
    Journal of the American Mathematical Society
  • 2019
We give a construction of contact homology in the sense of Eliashberg–Givental–Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of
New obstructions to symplectic embeddings
In this paper we establish new restrictions on the symplectic embeddings of basic shapes in symplectic vector spaces. By refining an embedding technique due to Guth, we also show that they are sharp.
Compactness results in Symplectic Field Theory
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic
Automatic transversality and orbifolds of punctured holomorphic curves in dimension four
We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of
The embedding capacity of 4-dimensional symplectic ellipsoids
This paper calculates the function $c(a)$ whose value at $a$ is the infimum of the size of a ball that contains a symplectic image of the ellipsoid $E(1,a)$. (Here $a \ge 1$ is the ratio of the area
Introduction to Symplectic Field Theory
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds
Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations
We study pseudoholomorphic maps from a punctured Riemann surface into the symplectization of a contact manifold. A Fredholm theory yields the virtual dimension of the moduli spaces of such maps in
...
1
2
...