Oleksandr Zadorozhnyi (Uni Potsdam)
Florian Bertrand (American University of Beirut), Francine Meylan (Uni Freiburg)
14:00 Florian Bertrand (American University of Beirut) : Analytic discs in Complex Analysis
15:30 Francine Meylan (University of Friburg, Switzerland):On some Rigidity properties of holomorphic maps
In this talk, I will present a survey on the method analytic discs in complex analysis. Initiated by Riemann and Hilbert, the method of analytic discs appeared later on as a powerful technique in Several Complex Variables with the works of Bishop, Lempert or Bedford-Gaveau. Such discs are indeed natural invariants and are particularly adapted to the study of geometric properties of domains and their holomorphic maps.
The following uniqueness theorem of Cartan serves as a starting point for this talk: Biholomorphic maps of a bounded domain in the complex space are uniquely determined by its value and first derivatives at a given point of the domain.
We will then address the following question: When is a bihomorphic map on a submanifold of the complex space uniquely determined by a its value and (possibly higher) derivatives at a given point of the manifold?