The purpose of this course is to give the participants a broad view of many areas that are subjects of active research in contemporary complex analysis of one variable, giving the students the basis to continue their studies deeper in any direction.
There is no required textbook for this course. Lecture notes (pdf-files) will be made available on the course web page. To access them, please click here.
The following are general references for various aspects of this course:
L.V. Ahlfors, Quasiconformal mappings, Van Nostrand, Princeton, 1966 (reprinted by Wadsworth, 1987).
L.V. Ahlfors, Conformal invariants, McGraw-Hill, New York, 1973.
A.F. Beardon, The geometry of discrete groups, Springer, New York, 1983.
A.F. Beardon, A primer on Riemann surfaces, Cambridge Univ. Press, 1984.
A.F. Beardon, Iteration of rational functions, Springer, New York, 1991.
C. Caratheodory, Theory of functions, Volume II, 2nd English ed., Chelsea, New York, 1954.
W.K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
W.K. Hayman and P.B. Kennedy, Subharmonic functions, vol. 1, Academic Press, London, 1976.
O. Lehto, Univalent functions and Teichmuller spaces, Springer, New York, 1987.
O. Lehto and K.I. Virtanen, Quasiconformal mappings in the plane, Springer, Berlin, 1973.
T. Ransford, Potential theory in the complex plane, Cambridge Univ. Press, 1995.
G. Springer, Riemann surfaces, 2nd ed., Chelsea, New York, 1957.