GT seminar: "Extremal Lagrangian tori in convex toric domains"

Abstract: Cieliebak and Mohnke define the symplectic area of a Lagrangian submanifold of a symplectic manifold as the minimal positive symplectic area of a 2-disk in the symplectic manifold with a boundary on the Lagrangian. I will explain that every Lagrangian torus that maximizes the symplectic area among the Lagrangian tori in the standard symplectic unit ball must lie entirely on the boundary of the ball. This answers a question attributed to L. Lazzarini and settles a conjecture of Cieliebak and Mohnke in the affirmative. I will also explain to which extent this statement is true for general toric domains.

This is a seminar in our Geometry and Topology seminar series.