Sufficient and necessary conditions for conformality at a point.Part I. Geometric viewpoints

摘要

We study the local behaviour of ACL-homeomorphisms in the plane,defined in a neighbourhood of a point and satisfying the Beltrami equationwith coefficient 111tH < I. We use extremal length techniques, modules ofring domains, of quadrilaterals and of families of curves that are arcsof spirals to provide geometric sufficient and necessary conditions forconformality at a point.