J-holomorphic Disks and Lagrangian Squeezing

Abstract

We define an invariant $l(M,W,ω)$ for Lagrangian submanifold and prove that if the Lagrangian submanifold is embedded in the ball of radius $r_0$, then $l(M,W,Ω)$ must be smaller than $4πt_0^2$. This improves Gromov's Lagrangian embedding theorem.