Geometric Characterization of Open image in new window-Conformal Mappings

  • K. GürlebeckEmail author
  • J. Morais


In this paper we study the description of monogenic functions in ℝ3 by their geometric mapping properties. The monogenic functions are considered at first as general quasi-conformal mappings. We consider the local mapping properties of a monogenic function and show that this class of functions can be defined as a special subclass of quasiconformal mappings. It is proved that monogenic functions with nonvanishing Jacobian determinant map infinitesimal balls onto special ellipsoids. The condition on the semiaxes of these ellipsoids is explicitly given.


Conformal Mapping Quasiconformal Mapping Mapping Property Monogenic Function Geometric Characterization 
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© Springer-Verlag London 2010

Authors and Affiliations

  1. 1.Institut für Mathematik/PhysikBauhaus-Universität WeimarWeimarGermany

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