Reading notes for Real and Complex Analysis

It’s just a note for books and other materials i’ve read during winter/sommer break in 2019 and for courses “Algebra and Complex Analysis”/“Analysis 3”/“Algebra II” at HU Berlin.

And it’s more likely to be my self-training for scientific writing,so it would have lots of mistaskes or looks like “not even wrong”.

~Keep Updating~

03/06 Artikel created,topics Bieberbach Conjecture and Riemann mapping theorem were added
07/28 The Topic “Measure and Integration” Updated
08/12 The Topic “ODE and Dynamical Systems” Upadated
08/12 The Topic “Integral on Mannifolds”

Bieberbach’s Conjecture

In the following,D means unit disk and S means the set of all schlicht(i.e. one-to-one holomorphic) functions.

“Vielleicht ist überhaupt $k_n = n$.”(L.Bieberbach,1916)

Mittag-Leffler Theorem,Weierstrass Factorization Theorem and Coherent Analytic Sheaf

From Riemann Mapping Theorem to Uniformization Theorem

Picard’s Theorem and Neavanlinna Theory