Complex geodesics and variational calculus for univalent functions
arXiv:1610.09564
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.
arXiv commentarXiv admin note: substantial text overlap with arXiv:1405.4830