Conformal mapping of o-minimal corners

摘要

We say that a simply connected domain in the plane has an o-minimal corner at the origin if its boundary at the origin is given by two curves forming a corner of nonzero angle which are definable in a given o-minimal structure. We investigate the mapping function at o-minimal corners. We describe the asymptotic behaviour if the boundary curves are definable in an arbitrary polynomially bounded o-minimal structure. If they are definable in the o-minimal structure R_(an)~R we establish an asymptotic expansion in terms of a generalized power series with logarithmic perturbation.