MA 324: Topics in Complex Analysis
Credits: 3:0
The general theory of holomorphic mappings between bounded domains, automorphisms of bounded domains, discussions on the non-existence of a classical Riemann Mapping Theorem in several variables, discussion of the various forms of the one-variable Riemann Mapping Theorem, the Rosay-Wong Theorem, other Riemann-Rosay-Wong-type results (e.g., the work of Pinchuk) to the extent that time permits.
Suggested books and references:
- Krantz, S. G., Geometric analysis and function spaces, CBMS Regional Conference Series in Mathematics, 81 (A M S, Providence, USA).
- Rudin, W., Function theory in the unit ball of $\mathbb{C^n}$, Grundlehren der Mathematischen Wissenschaften (Springer-Verlag, New York-Berlin, 1980).
- Krantz., S. G., Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001.