Liouville polarizations and the rigidity of their Lagrangian skeleta in dimension $4$

Abstract

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 symplectic embedding results that answer a question by Sackel-Song-Varolgunes-Zhu and Brendel, new Lagrangian non-removable intersections at small scales, and a novel phenomenon of Legendrian barriers in contact geometry.

54 pages, 13 figures. Final version, to be published by ASENS