Defense of dissertation in the field of mathematics, M.Sc. Stavros Evdoridis

Title of the doctoral thesis is "Geometric properties of harmonic and polyharmonic mappings"

This dissertation is part of the Mathematical Analysis area and the main topic is the study of the behaviour of two classes of complex functions, namely the harmonic and the polyharmonic mappings. The primary goal of the dissertation was to obtain analogues of well-known results, originally proved for the class of analytic functions, for harmonic and polyharmonic mappings. Another significant part of it concerns the investigation of the boundary behaviour of the abovementioned mappings, mainly defined it the unit disc. Polyharmonic mappings, and especially their subclass known as biharmonic mappings, have connections with scientific fields such as Physics and Engineering. Although the application of the obtained results is not part of this study, some of them could be proved to be useful to the experts of these fields in the future.

One of the main results of this dissertation is the generalisation of the Radó theorem to the class of polyharmonic mappings. In our theorem we prove that there is no polyharmonic mapping of the unit disc onto the whole complex plane. Other results concern the famous Bohr theorem, presenting improved versions for both the analytic and the harmonic case as well as theorems about the boundary behaviour and the continuity of the boundary function of harmonic and polyharmonic mappings. In the latter case, certain conditions are obtained in order for the boundary function of a harmonic (or polyharmonic) mapping of the unit disc to be continuous at a single point.

Opponent is Associate Professor María-José Martín-Gómez, Universidad de La Laguna, Spain

Custos is Professor Juha Kinnunen, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral candidate: [email protected], +358417536149

The public defence will be organised via Zoom. Link to the event

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The dissertation is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic dissertation

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