Higher asymptotics of the complex Monge-Ampère equation
We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.
We establish the homotopy classification of holomorphic submersions from Stein manifolds to Complex manifolds satisfying an analytic property introduced in the paper. The result is a holomorphic analogue of the Gromov--Phillips theorem on smooth submersions.