MTH-21c.4 Advanced Complex Analysis
Syllabus
- Entire functions: order of growth, Jensen’s formula, Hadamard factorization, Phragmen-Lindelof method, basics of Nevanlinna theory.
- Conformal maps, boundary regularity of Riemmann maps, univalent functions, harmonic measure.
- Normal families of holomorphic functions on the sphere, Zalcman’s rescaling principle and applications to complex dynamics.
- The hyperbolic metric in the unit disk, non-euclidean geometry, invariant form of Schwarz lemma, conformal invariance, general metrics in complex analysis.