16 citations · 48 across the 15 of their papers we have counts for
15 papers
Liouville polarizations and the rigidity of their Lagrangian skeleta in dimension
Emmanuel Opshtein, Felix Schlenk
The main theme of this paper is the introduction of a new type of polarizations, suited for some open symplectic manifolds, and their applications. These applications include sympl…
Symplectic Camel theorems and -rigidity of coisotropic submanifolds
Emmanuel Opshtein
This paper deals with the -rigidity of the reduction of coiostropic submanifolds under the action of symplectic homeomorphism. More precisely, we exhibit several si…
Quantitative -principle in symplectic geometry
Lev Buhovsky, Emmanuel Opshtein
We prove a quantitative -principle statement for subcritical isotropic embeddings. As an application, we construct a symplectic homeomorphism that takes a symplectic disc into a…
Squeezing Lagrangian tori in dimension 4
Richard Hind, Emmanuel Opshtein
We find the minimal size of 4 dimensional balls and polydisks into which product Lagrangian tori can be mapped by a Hamiltonian diffeomorphism.
-rigidity of Lagrangian submanifolds and punctured holomorphic discs in the cotangent bundle
Cedric Membrez, Emmanuel Opshtein
Our main result is the -rigidity of the area spectrum and the Maslov class of Lagrangian submanifolds. This relies on the existence of punctured pseudoholomorphic di…
Quantitative -principle for isotropic embeddings and applications to -symplectic geometry
Lev Buhovsky, Jaime Bustillo, Emmanuel Opshtein
We prove here a quantitative -principle statement that applies to isotropic embeddings of discs. We then apply it to get -flexibility and rigidity results in symplectic geo…