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Existence of close pseudoholomorphic disks for almost complex manifolds and their application to the Kobayashi-Royden pseudonorm. (English. Russian original) Zbl 0967.32024
Funct. Anal. Appl. 33, No. 1, 38-48 (1999); translation from Funkts. Anal. Prilozh. 33, No. 1, 46-58 (1999).
Let we have a pseudoholomorphic disk of radius \(R\) and an almost complex manifold. It pass through a fixed point and tangent to a given vector \(v\) at this point. For any \(\varepsilon\) there is a neighborhood \(U\) of the vector \(v\) such that we can find a pseudoholomorphic disk of radius \(R - \varepsilon\) going through the same point and tangent to a vector from \(U\).
This result has several interesting applications, particularly, the author’s coincidence of the pseudo-distance defined by the Kobayashi-Royden pseudonorm with the Kobayashi pseudodistance.

MSC:
32Q60 Almost complex manifolds
32F45 Invariant metrics and pseudodistances in several complex variables
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