### 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:

1. Krantz, S. G., Geometric analysis and function spaces, CBMS Regional Conference Series in Mathematics, 81 (A M S, Providence, USA).
2. Rudin, W., Function theory in the unit ball of $\mathbb{C^n}$, Grundlehren der Mathematischen Wissenschaften (Springer-Verlag, New York-Berlin, 1980).
3. Krantz., S. G., Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 09 Dec 2022