Connectedness and complex-dilatation characterization of the global chord-arc locus

Characterize the connectedness of the space of chord-arc curves within the BMO-Teichmüller space and determine the corresponding characterization of its complex dilatations.

Background

The paper establishes a global analytic characterization of chord-arc curves through invertibility of the analytic projection associated with a conformal welding. It does not resolve the broader structure of the chord-arc locus in BMO-Teichmüller space. In particular, the connectedness of that locus and an intrinsic description of the complex dilatations representing it are identified as unresolved aspects of the theory.