Grunsky operator, Grinshpan's conjecture and universal Teichmuller space

2022/05/17 by Samuel L. Krushkal, Krushkal, Samuel L.
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2205.08519

openalex publication_date 2022/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A. Grinshpan posed a deep conjecture on the norm of the Grunsky operator generated by univalent functions in the disk. It gives a quantitative answer in terms of the Grunsky coefficients, to which extent a univalent function determines the bound of dilatations of its quasiconformal extensions. We provide the proof of this conjecture and its various analytic, geometric and potential applications. Another result concerns the model of universal Teichmuller space by Grunsky coefficients.

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