Complex geodesics and variational calculus for univalent functions
Samuel L. Krushkal
TL;DR
This paper explores the intrinsic link between complex geodesics in Teichmüller spaces and variational calculus for univalent functions, revealing new distortion results and phenomena in geometric function theory.
Contribution
It establishes a novel connection between Teichmüller space geodesics and variational calculus, leading to new insights and distortion theorems for univalent functions.
Findings
Deep distortion results for functions with quasiconformal extensions
Identification of new phenomena in geometric function theory
Geometric features influencing function behavior
Abstract
It turns out that complex geodesics in Teichm\"uller 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.
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Taxonomy
TopicsAnalytic and geometric function theory · Advanced Numerical Analysis Techniques · Numerical methods in inverse problems