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.
@article{1480,
title = {On mapping properties of monogenic functions},
journal = {CUBO, A Mathematical Journal},
volume = {11},
year = {2009},
language = {en},
url = {http://dml.mathdoc.fr/item/1480}
}
Gürlebeck, K.; Morais, J. On mapping properties of monogenic functions. CUBO, A Mathematical Journal, Tome 11 (2009) . http://gdmltest.u-ga.fr/item/1480/