TY - JOUR

T1 - A reverse isoperimetric inequality for J-holomorphic curves

AU - Groman, Yoel

AU - Solomon, Jake P.

N1 - Publisher Copyright:
© 2014, Springer Basel.

PY - 2014/9/1

Y1 - 2014/9/1

N2 - 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 2π for the Lagrangian submanifold RPn ⊂ CPn. 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.

AB - 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 2π for the Lagrangian submanifold RPn ⊂ CPn. 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.

UR - http://www.scopus.com/inward/record.url?scp=84907692365&partnerID=8YFLogxK

U2 - 10.1007/s00039-014-0295-2

DO - 10.1007/s00039-014-0295-2

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AN - SCOPUS:84907692365

SN - 1016-443X

VL - 24

SP - 1448

EP - 1515

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 5

ER -