Geometric aspects of complex harmonic mappings

13 junio, 2019 -

• Proy-Investigacion

Tipo de Proyecto: Fondecyt Regular 2019
Investigador Responsable: Rodrigo Hernández Reyes (UAI)
Co-Investigador: Osvaldo Venegas Torres.
Unidad Académica: Departamento de Ciencias Matemáticas y Fïsicas.
Tiempo de Ejecución: 2019 – 2022

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Abstract

The study of Geometric Function Theory had its peak during the 20th century and naturally extending towards complex harmonic functions, being these the topic of a long list of works impulsed greatly by Clunie and Sheild-Small’s work and P.L Duren’s book. These investigations did not only stay in the complex plane, but were also extended in the several complex variables world. A glance of this is given in the book by I. Graham and G. Kohr, in which many geometrical phenomena for planar analytic functions are extended to holomorphic mappings f: C^n  C^n.

Specifically, we propose to study some geometric aspects of harmonic functions in one and several complex variables, which we can set forth as follows:

1. Always convex harmonic mappings in the plane.

2. Growth of convex harmonic mappings in the plane

3. Schwarzian norm of functions in CH

4. Preschwarzian derivatives and their properties for pluriharmonic mappings

5. Schwarzian derivatives and their properties for pluriharmonic mappings

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