Modular Equations and Distortion Functions
Complex Variables
2008-05-11 v1 Classical Analysis and ODEs
Abstract
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.
Cite
@article{arxiv.math/0701228,
title = {Modular Equations and Distortion Functions},
author = {G. D. Anderson and S. -L. Qiu and M. Vuorinen},
journal= {arXiv preprint arXiv:math/0701228},
year = {2008}
}
Comments
23 pages