Department of Mathematics, Morehouse College, Atlanta, Georgia 30314 ; Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Abstract:
A well-known characterization of quasicircles is the following: A Jordan curve in the complex plane is a quasicircle if and only if it is the image of the unit circle under a quasisymmetric embedding. In this paper we try to characterize a subclass of quasicircles, namely, symmetric quasicircles, by introducing the concept of asymptotically symmetric embeddings. We show that a Jordan curve in the complex plane is a symmetric quasicircle if and only if it is the image of the unit circle under an asymptotically symmetric embedding.