1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

LECTURE 4. THE NONSQUEEZING THEOREM AND CAPACITIES 27

found in some of the articles in Audin-Lafontaine [AL].) In the next lecture we will
sketch the outlines of a rather different approach using standard elliptic analysis.

Exercise 4.6. Let (V, w, J) be a symplectic vector space with compatible almost
complex structure J and associated inner product 9J. Given two vectors v, w · denote
by P(v,w) the parallelogram they span. Show that

w(v, w) :::; 9J-area of P(v, w)

with equality if and only if w = Jv. Deduce that J-holomorphic curves in (M, w, J)

are 9J-minimal surfaces.