The fredholm eigenvalues of plane domains

Abstract

The problem of how the Fredholm eigenvalue δ(D) of a simply connected domain D varies under “small” perturbations of D has been much studied. The difficulty consists in determining the sense in which such a perturbation is small. Here we consider a metric which arises in the definition of universal Teichmuller space. We show that, with this metric, the Fredholm eigenvalue δ(D) is a locally Lipschitz function of D, if D is a quasiconformal disk.