Course: MAT 485 2.0 Univalent Functions and Conformal Mapping (Optional)
Course content:
Univalent functions. Complex Modules and Extremal Lengths. Basic properties of modules. Some special modules. Uniqueness lemmas. Reduced module. Applications. Statement of the General Coefficient Theorem. Circular, radial, and spiral slit mappings. Parallel slit mappings. Local structure of the trajectories. Global structure of the trajectories on a finite oriented Riemann surface.
Recommended Readings:
- Conformal invariants. Topics in geometric function theory. Reprint of the 1973 original; 2010, by Lars V. Ahlfors;
- Univalent Functions and Conformal Mapping, Springer-Verlag. Berlin, 1958 by James A. Jenkins
- Quadratic Differentials. Springer-Verlag, Berlin, 1984, by Kurt Strebel.
- Gamelin,T.W. (2001). Complex Analysis. Spring.
- Philips, E.G. (1940). Complex Variables. Dover Books.Conway, John B. (1973). Functions of one complex variable. Spring.
- Ponnusamy, S.(2011). Functions of complex Analysis. Norosa.