A reverse isoperimetric inequality for Jholomorphic curves.
A reverse isoperimetric inequality for Jholomorphic curves.

Jake Solomon , Hebrew University
Fine Hall 401
I'll discuss a bound on the length of the boundary of a Jholomorphic curve with Lagrangian boundary conditions by a constant times its area. The constant depends on the symplectic form, the almost complex structure, the Lagrangian boundary conditions and the genus. A similar result holds for the length of the real part of a real Jholomorphic curve. The infimum over J of the constant properly normalized gives an invariant of Lagrangian submanifolds. The invariant is $2\pi$ for the Lagrangian submanifold $RP^n \subset CP^n.$ The bound can also be applied to prove compactness of moduli of Jholomorphic curves to asymptotically exact targets. These results are joint work with Yoel Groman.