Analytic Function With Quasiconformal Deformation Extensions And Its Grunsky Type Inequality

We define the Grunsky coefficients for an analytic function in the exterior of the unit disk and discuss these coefficients when the function can be extended to a quasiconformal deformation in the whole plane. We also define the Grunsky operator for such an analytic function and discuss some basic properties of the Grunsky operator.