ENGLISH

Geometric Function Theory: A Second Course in Complex Analysis

By Tom Carroll

Book information

Publisher
Springer Nature Switzerland
Year
2024
ISBN
9783031737268, 9783031737275
DOI
10.1007/978-3-031-73727-5
ISSN
2197-4144
Language
english
Format
PDF
Filesize
7 MB (7289462 bytes)
Series
Springer Undergraduate Mathematics Series
Edition
1
Pages
353\358
Topic
Mathematics\\Analysis
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2024-12-13 13:08:32
Carathéodory ConvergenceConformal MappingsHyperbolic Geometrynormal familiesRiemann Mapping TheoremRiemann SphereRunge's TheoremUniformizationUnivalent Functions

Description

This textbook provides a second course in complex analysis with a focus on geometric aspects. It covers topics such as the spherical geometry of the extended complex plane, the hyperbolic geometry of the Poincaré disk, conformal mappings, the Riemann Mapping Theorem and uniformisation of planar domains, characterisations of simply connected domains, the convergence of Riemann maps in terms of Carathéodory convergence of the image domains, normal families and Picard's theorems on value distribution, as well as the fundamentals of univalent function theory. Throughout the text, the synergy between analysis and geometry is emphasised, with proofs chosen for their directness. The textbook is self-contained, requiring only a first undergraduate course in complex analysis. The minimal topology needed is introduced as necessary. While primarily aimed at upper-level undergraduates, the book also serves as a concise reference for graduates working in complex analysis.

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