On mapping properties of monogenic functions
- K. Gürlebeck guerlebe@fossi.uni-weimar.de
- J. Morais jmorais@mat.ua.pt
Downloads
Abstract
Main goal of this paper is to study the description of monogenic functions by their geometric mapping properties. At first monogenic functions are studied as general quasi-conformal mappings. Moreover, dilatations and distortions of these mappings are estimated in terms of the hypercomplex derivative. Then pointwise estimates from below and from above are given by using a generalized Bohr‘s theorem and a Borel-Carathéodory theorem for monogenic functions. Finally it will be shown that mono- genic functions can be defined as mappings which map infinitesimal balls to special ellipsoids.
Keywords
Most read articles by the same author(s)
- S. Georgiev, J. Morais, W. Spross, New Aspects on Elementary Functions in the Context of Quaternionic Analysis , CUBO, A Mathematical Journal: Vol. 14 No. 1 (2012): CUBO, A Mathematical Journal