The Grunsky operator and quasiconformality: old and new

Abstract

The Grunsky operator arises from univalence and plays a crucial role in geometric function theory. This operator also implies quasiconformal extendibility and has an intrinsic connection with Teichmuller space theory and its interactions with complex analysis and pluripotential theory. This paper surveys recent results in this field and simultaneously provides solutions of two old problems.

arXiv admin note: text overlap with arXiv:2205.08519