Geometric Function Theory - Tom Carroll

Geometric Function Theory

A Second Course in Complex Analysis

(Autor)

Buch | Softcover
X, 333 Seiten
2025
Springer International Publishing (Verlag)
978-3-031-73726-8 (ISBN)
58,84 inkl. MwSt

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.

Tom Carroll is Senior Lecturer in Mathematics at University College Cork. He is the author of over 40 research papers, primarily in the general areas of functions of a complex variable, probability theory and stochastic processes, and partial differential equations. Tom has served as President of the Irish Mathematical Society (2021-2022) and has recently been appointed editor of the Society's Bulletin.

1 Introduction.- 2 The Complex Plane - Preparatory Topics.- 3 The Riemann Sphere.- 4 The Hyperbolic Disk.- 5 Normal Families and Value Distribution.- 6 Simply Connected Domains and the Riemann Mapping Theorem.- 7 Runge's Theorem and Further Characterisations of Simply Connected Domains.- 8 Univalent Functions - the Basics.- 9 Carathéodory Convergence of Domains and Hyperbolic Geodesics.- 10 Uniformisation of Planar Domains.

Erscheint lt. Verlag 18.1.2025
Reihe/Serie Springer Undergraduate Mathematics Series
Zusatzinfo XI, 322 p. 60 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Carathéodory convergence • conformal mapping • hyperbolic geodesic • Hyperbolic Geometry • Meromorphic Function • normal families • Picard Theorem • Riemann sphere • Runge's theorem • Schwarz-Pick • uniformization of planar domains • univalent functions
ISBN-10 3-031-73726-1 / 3031737261
ISBN-13 978-3-031-73726-8 / 9783031737268
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch (2022)
Springer Spektrum (Verlag)
79,99