Cheraghi D. Geometric Complex Analysis

London: Imperial College, 2017. — 98 p.The actual prerequisite for this course is quite minimal. We assume that the students taking this class are familiar with the notions of holomorphic maps and their basic properties. This is a concise math course with "epsilon- delta" proofs, and so precise forms of definitions and statements appear in the notes. To rectify the challenge of where we start, we have summarized in Chapter 1 (in three pages) the basic results from complex analysis that we will rely on. These notes were prepared for the course "Geometric Complex Analysis" for the autumn term of 2016 at Imperial College London.Preliminaries from complex analysis.
Schwarz lemma and automorphisms of the disk.
Riemann sphere and rational maps.
Conformal geometry on the disk.
Conformal Mappings.
Growth and Distortion estimates.
Quasi-conformal maps and Beltrami equation.
Appendix.