Existence of close pseudoholomorphic disks for almost complex manifolds and their application to the Kobayashi-Royden pseudonorm
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.
scientific article; zbMATH DE number 1407612
scientific article