Symplectic embeddings of polydisks
Article
First Online:
Received:
Accepted:
- 212 Downloads
- 17 Citations
Abstract
If P and P ′ are symplectic polydisks of radii R 1≤...≤R n and R 1 ′≤...≤R n ′, respectively, then we prove that P symplectically embeds in P ′ provided that C(n)R 1≤R 1 ′ and C(n)R 1...R n ≤R 1 ′...R n ′. Up to a constant factor, these conditions are optimal.
Keywords
Boundary Component Symplectic Form Double Point Main Lemma Symplectic Geometry
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Ekeland, I., Hofer, H.: Symplectic topology and Hamiltonian dynamics. Math. Z. 200(3), 355–378 (1989)MATHCrossRefMathSciNetGoogle Scholar
- 2.Gromov, M.: Pseudoholomorphic curves in symplectic manifolds. Invent. Math. 82(2), 307–347 (1985)MATHCrossRefMathSciNetGoogle Scholar
- 3.Gromov, M.: Filling Riemannian manifolds. J. Differ. Geom. 18(1), 1–147 (1983)MATHMathSciNetGoogle Scholar
- 4.Guth, L.: The width-volume inequality. arXiv:math/0609569Google Scholar
- 5.Hofer, H.: Symplectic capacities. In: Geometry of Low-dimensional Manifolds 2 (Durham, 1989). Lond. Math. Soc. Lect. Note Ser., vol. 151, pp. 15–34. Cambridge Univ. Press, Cambridge (1990)Google Scholar
- 6.Cieliebak, K., Hofer, H., Latschev, J., Schlenk, F.: Quantitative symplectic geometry. arXiv:math/0506191Google Scholar
- 7.Moser, J.: On the volume element of a manifold. Trans. Am. Math. Soc. 120, 286–294 (1965)MATHCrossRefGoogle Scholar
- 8.Schlenk, F.: Embedding Problems in Symplectic Geometry. de Gruyter Expositions in Mathematics, vol. 40. Walter de Gruyter, Berlin (2005)MATHGoogle Scholar
- 9.Traynor, L.: Symplectic packing constructions. J. Differ. Geom. 42(2), 411–429 (1995)MATHMathSciNetGoogle Scholar
Copyright information
© Springer-Verlag 2008