The Local Theory

Norbert Steinmetz ()
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Norbert Steinmetz: TU Dortmund, Department of Mathematics

Chapter 3 in Lectures on Complex Analysis, 2026, pp 59-81 from Springer

Abstract: Abstract The local theory is among the most fascinating areas of complex analysis. In a remarkable sequence of theorems–each with elegant and surprisingly simple proofs relying solely on Cauchy’s fundamental results–we deduce the local properties of holomorphic functions. Central topics include open mappings, the maximum principle, hyperbolic geometry, proper mappings, and normal families.

Date: 2026
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DOI: 10.1007/978-3-032-13996-2_3

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