Joint IAS/Princeton University Symplectic Geometry Seminar

I'll discuss a bound on the length of the boundary of a J-holomorphic 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 J-holomorphic 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 J-holomorphic curves to asymptotically exact targets. These results are joint work with Yoel Groman.