Regularity and estimates for $J$-holomorphic discs attached to a maximal totally real submanifold

Mathematics – Complex Variables

Scientific paper

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20 pages, 2 figures

Scientific paper

We prove that pseudo-holomorphic discs attached to a maximal totally real
submanifold inherit their regularity from the regularity of the submanifold and
of the almost complex structure. The proof is based on the computation of an
explicit lower bound for the Kobayashi metric in almost complex manifolds,
which also yields explicit estimates of H\"olderian norms of such discs.

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