Holomorphic maps on complex manifolds: two perspectives

15.07.2020, 14:00  –  Campus Golm, Haus 9, Raum 2.22
Institutskolloquium

Florian Bertrand (American University of Beirut), Francine Meylan (Uni Freiburg)

If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.

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

Florian Bertrand (American University of Beirut) : Analytic discs in Complex Analysis

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.

Francine Meylan (University of Friburg, Switzerland): On some Rigidity properties of 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?