Complex Analysis, Riemann Surfaces and Integrable Systems (eBook, PDF)

Complex Analysis, Riemann Surfaces and Integrable Systems (eBook, PDF)

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This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems o...

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