期刊
GEOMETRIC AND FUNCTIONAL ANALYSIS
卷 24, 期 5, 页码 1448-1515出版社
SPRINGER BASEL AG
DOI: 10.1007/s00039-014-0295-2
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资金
- Israel Science Foundation [1321/2009]
- Marie Curie International Reintegration Grant [239381]
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 for the Lagrangian submanifold 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.
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