On mapping properties of monogenic functions

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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

monogenic functions , quasi-conformal mappings , geometric mapping properties
  • K. Gürlebeck Institute of Mathematics / Physics, Bauhaus-University, Weimar, Germany.
  • J. Morais Institute of Mathematics / Physics, Bauhaus-University, Weimar, Germany.
  • Pages: 73–100
  • Date Published: 2009-03-01
  • Vol. 11 No. 1 (2009): CUBO, A Mathematical Journal

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Published

2009-03-01

How to Cite

[1]
K. Gürlebeck and J. Morais, “On mapping properties of monogenic functions”, CUBO, vol. 11, no. 1, pp. 73–100, Mar. 2009.

Issue

Vol. 11 No. 1 (2009): CUBO, A Mathematical Journal

Section

Articles