Complex geodesics and variational calculus for univalent functions

2016/10/29 by Samuel L. Krushkal, Krushkal, Samuel L. · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1610.09564

openalex publication_date 2016/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It turns out that complex geodesics in Teichmüller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features associated to these metrics and geodesics provide deep distortion results for various classes of functions with quasiconformal extensions and create new phenomena which do not appear in the classical geometric function theory.

Cited by

• Towards a general distortion theory for univalent functions: Teichmuller spaces and coefficient problems of complex analysis

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