Journal of Symplectic Geometry

Volume 18 (2020)

Number 3

Coisotropic Hofer–Zehnder capacities and non-squeezing for relative embeddings

Pages: 819 – 865



Samuel Lisi (Department of Mathematics, University of Mississippi, Oxford, Miss., U.S.A.)

Antonio Rieser (Centro de Investigación en Matemáticas (CIMAT), Centro de Investigación en Matemáticas, Guanajuato, Gto., Mexico)


We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the Hofer–Zehnder capacity. As a consequence, we obtain a non-squeezing theorem for symplectic embeddings relative to coisotropic constraints and existence results for leafwise chords on energy surfaces.

This work was supported in part by the ERC Starting Grant of Frédéric Bourgeois StG-239781-ContactMath, the ERC Starting Grant of Vincent Colin Geodycon, the Israel Science Foundation grant 723/10, the ERC 2012 Advanced Grant 20120216 of Robert Adler, Short Visit Grants from the Contact and Symplectic Topology Research Network of the European Science Foundation, and Catédras CONACYT / 1076.

Received 25 September 2017

Accepted 16 July 2019

Published 30 July 2020