Geometric Function Theory Explorations in Complex Analysis /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Krantz, Steven G. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2006.
• Series: Cornerstones
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Harmonic analysis.; Functions of complex variables.; Partial differential equations.; Potential theory (Mathematics).; Differential geometry.; Analysis.; Functions of a Complex Variable.; Abstract Harmonic Analysis.; Differential Geometry.; Partial Differential Equations.; Potential Theory.

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 grou...

Table of Contents:

• 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
• 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
• Algebraic Topics
• Automorphism Groups of Domains in the Plane
• Cousin Problems, Cohomology, and Sheaves.