Thesis

• Ph.D. Thesis title:

"Conformal invariants in the complex plane and the Hardy number of conformal maps"

Abstract:

My research concerns classical problems in complex analysis and geometric function theory such as properties of conformal invariants and relations between them. The most important and well-studied conformal invariants in the complex plane are harmonic measure, hyperbolic distance, Green's function and extremal length or modulus. Also, I find the Hardy number of a region by looking at its geometric properties and I prove necessary and sufficient geometric conditions for whether a conformal mapping of the unit disk belongs to some Hardy space. Actually, I establish such conditions by studying harmonic measure and hyperbolic distance. My motivation to study such problems was some open questions posed by Poggi-Corradini in his thesis in 1996.

Full-text in greek with an english overview: Ph.D. file

• M.Sc. Thesis title:

"Conformal invariants in the complex plane and relations between them"

Full-text in greek: M.Sc. file