Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reverse isoperimetric inequality for J-holomorphic curves   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 $2\pi$ 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.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th