Geometric Function Theory

Mark Elin, Marina Levenshtein, David Shoikhet, Fiana Yacobzon, Dov Aharonov (Technion), Lev Aizenberg (Bar-Ilan University), Vladimir Bolotnikov (College William and Mary, USA), Nikolai Tarkhanov (Universität Potsdam, Germany) and Lawrence Zalcman (Bar-Ilan University)
Geometric function theory focuses on the geometric properties of univalent mappings. This subject has been examined with changing emphasis for over a hundred years. Well-known results in this field include the Riemann mapping theorem, hyperbolic geometry, the Schwarz Lemma, the Julia-Wolff-Caratheodory Theorem and others.
Our research focuses on biholomorphic mappings on a unit ball (in one-dimensional and multi-dimensional complex spaces). We study the geometric structures of these mappings, including starlike and spiral-like mappings with respect to an interior point or a boundary point, convex functions in one direction and so on. Geometric characteristics of images involve distortion and covering theorems and boundary behavior of different classes of mappings, as well as interpolation problems.