Three-cornered hat harmonic functions

Abstract

Let be a harmonic function in the unit disc, where f and g are holomorphic functions and g′(z) = zf′(z). We obtain a simple sufficient condition on f for the harmonic function h to be univalent and its image to be a three-cornered hat domain.

Keywords:

• harmonic function
• univalent function
• three-cornered hat domain

AMS Subject Classification::

• Primary: 30C45

Acknowledgement

This work was partially supported by Romanian Ministry of Education and Research CNCSIS Grant type A, 1472/2007.