Contributed Talk


A geometric approach to problems in theories of monogenic functions


Manh Hung Nguyen
Bauhaus-Universitaet Weimar, Germany

Abstract

Theories of monogenic functions are developed as generalizations of the theory of holomorphic functions in the complex plane. With these theories, the highlights of the complex function theory for the treatment of boundary value problems of partial differential equations are transferred to higher dimensional spaces. Basically, monogenic function theories are based on the generalizations of the (complex) Cauchy-Riemann operator. This leads to some problems, for example, the product of two monogenic functions or the composition of a monogenic with a Möbius transformation is no longer monogenic. The present paper introduces a geometric approach to study several problems arising from theories of monogenic functions.



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