Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Geometric Function Theory - Explorations in Complex Analysis

Geometric Function Theory

Explorations in Complex Analysis

Series: Cornerstones

Krantz, Steven G.

2006, XIII, 314 p.

A product of Birkhäuser Basel
Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-0-8176-4440-6

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-0-8176-4339-3

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem.

The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme.

This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works.

Content Level » Research

Keywords » Complex analysis - Green's function - Poisson kernel - Potential theory - Schwarz lemma - calculus - differential equation - harmonic analysis - measure - partial differential equation

Related subjects » Birkhäuser Mathematics

Table of contents 

* Preface Part I: Classical Function Theory * Invariant Geometry * Variations on the Theme of the Schwarz Lemma * Normal Families * The Riemann Mapping Theorem and its Generalizations * Boundary Regularity of Conformal Maps * The Boundary Behavior of Holomorphic Functions Part II: Real and Harmonic Analysis * The Cauchy–Riemann Equations * The Green's Function and the Poisson Kernel * Harmonic Measure * Conjugate Functions and the Hilbert Transform * Wolff's Proof of the Corona Theorem Part III: Algebraic Topics * Automorphism Groups of Domains in the Plane * Cousin Problems, Cohomology, and Sheaves * Bibliography * Index

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Analysis.

Additional information