One generalization of the class of helical functions

This paper is devoted to the study of domains whose boundaries are attainable by one-parametric families of curves formed by the rotation of a curve specially chosen for every family. We establish characteristics of analytic functions that map the unit circle on these domains. In addition, we single out subclasses of domains with rectifiable quasiconformal boundaries. We establish certain sufficient conditions for the univalence of functions that are analytic in mentioned domains.