Seminar

Analysis & Applications Seminar

Picard`s theorem and the range of harmonic maps

Speaker:  José González Llorente (Universidad Complutense de Madrid)
Date:  Friday, 08 October 2021 - 11:30
Place:  Aula 520, Departamento de Matemáticas (UAM) & online: us06web.zoom.us/j/89903037995

Abstract:

Picard’s (little) theorem is one of the most striking results of classical Complex Analysis. Since Picard’s original proof, a great variety of approaches, generalizations and surprising links with other areas have contributed to enrich the scope of Geometric Function Theory.
Motivated by extensions of Picard’s theorem to quasiregular mappings, J. Lewis obtained in 1994 the first purely real, harmonic proof of Picard’s little theorem.
In the talk we will report several variations on Picard’s theorem, with special emphasis on Lewis approach. In this direction, we will discuss a recent extension in terms of the range of harmonic maps in the plane.