A reverse isoperimetric inequality for J-holomorphic curves |
| |
Authors: | Yoel Groman Jake P. Solomon |
| |
Affiliation: | 1. Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel
|
| |
Abstract: | We prove that the length of the boundary of a J-holomorphic curve with Lagrangian boundary conditions is dominated 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. We calculate this invariant to be ({2pi}) for the Lagrangian submanifold ({mathbb{R} P^n subset mathbb{C} P^n.}) We apply our result to prove compactness of moduli of J-holomorphic maps to non-compact target spaces that are asymptotically exact. In a different direction, our result implies the adic convergence of the superpotential. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|