Quasicircles and hyperbolic zero packing

Abstract

We look at the work of Oleg Ivrii connected with the dimension of quasicircles for asymptotically small quasiconformality parameter $k$. We intend to make this work more easily accessible. Our main focus is the integral means spectrum associated with normalized conformal mappings of the exterior disk which have quasiconformal extensions to the whole plane with small dilatation parameter $k$. Moreover, we address the estimates from above only, not the sharpness from below.