# $J$-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

- Mathematics
- 2017

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

- Mathematics
- 2021

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

- MathematicsInventiones mathematicae
- 2018

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

- Mathematics
- 2017

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

- Mathematics
- 2015

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 ${\mathbb {P}^2}$

- MathematicsCompositio Mathematica
- 2007

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

- MathematicsJournal 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

- Mathematics
- 2014

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

- Mathematics
- 2003

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

- Mathematics
- 2008

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

- Mathematics
- 2009

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

- Mathematics, Physics
- 2000

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

- Mathematics
- 2004

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…