Journal of Symplectic Geometry

Volume 18 (2020)

Number 5

$J$-holomorphic cylinders between ellipsoids in dimension four

Pages: 1221 – 1245



Richard K. Hind (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)

Ely Kerman (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)


We establish the existence of regular $J$‑holomorphic cylinders in $4$‑dimensional ellipsoid cobordisms that are asymptotic to Reeb orbits of small Conley–Zehnder index. We also give an independent proof of the existence of cylindrical holomorphic buildings in $4$‑dimensional ellipsoid cobordisms under fairly general conditions.

Both authors are supported by grants from the Simons Foundation.

Received 7 August 2017

Accepted 20 November 2019

Published 29 October 2020