On the Modulus of a Union of Nested Annuli

Abstract

We prove a result which gives sufficient conditions for a conformal annulus which is a countable union of nested conformal annuli to have bounded modulus. Our theorem also gives estimates for the modulus of such an annulus and is proved using an interpolation result which constructs a quasiconformal map between two annuli given a smooth identification of their boundaries.

This paper has been withdrawn as it has been brought to the attention of the author that a result similar to Theorem 1 was proved in a paper of Lehto in 1965