Embedding Problems in Symplectic Geometry

By F. Schlenk. 2005

130 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7976eab8e19617222ab7f022ca88ab5d7a8170ae

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Symplectic embeddings into four‐dimensional concave toric domains (2013, methodology): “Moreover, the “symplectic folding” method from [14] can be used to construct examples of symplectic embeddings E(a, 1) → Z(λ, λb) where E(a, 1) 6⊂ Z(λ, λb) and also vol(E(a, 1)) > vol(B(λb)), so that E(a, 1) does not symplectically embed into the ball B(λb) alone.”
Symplectic embeddings of polydisks (2007, background): “The known results are discussed in detail in [6], and many other embedding problems are discussed in [8].”
Symplectic embeddings of 4‐dimensional ellipsoids (2008, background): “I also thank Tolman for giving me an advance copy of her paper [25], Schlenk for his encouragement and useful comments, and the referree for pointing out various small inaccuracies.”
THE SHARP ENERGY-CAPACITY INEQUALITY (2008, background): “Contrastingly, for any r > 1 there is > 0 such that B(2)( )×B(2)(r)(2) embeds symplectically in B(2)(1)(3) (this follows from the h-principle as in [25], 1.”
Beyond ECH capacities (2014, background): “If a > 2 , then “symplectic folding” can be used to symplectically embed P . a ; 1 / into B . c / whenever c > 2 C a = 2 ; see Schlenk [21, Proposition 4.3.9].”
The Restricted Three-Body Problem and Holomorphic Curves (2018, background): “Starting with Gromov’s celebrated non-squeezing theorem [104] the question which symplectic manifolds can be symplectically embedded into each other is a highly active area of research, see for example [213, 214] for a survey.”
Quantitative symplectic geometry (2005, unknown): “On Ell(4) , nonlinear symplectic embeddings (”folding”) yield additional constraints which are still not completely known; see [88] for the presently known results.”
The Gromov width of 4-dimensional tori (2011, background): “Computations and estimates of the Gromov width for various examples can be found in [4, 5, 6, 15, 18, 19, 21, 22, 29, 34, 38, 41, 42].”
Symplectic embedding problems, old and new (2017, background): “2The book [96] from 2005, for instance, is already completely outdated.”