Handbook of Complex Analysis Geometric Function Theory volume 1 1st Edition by Reiner Kuhnau 9780444828453 0444828451
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ISBN 10: 0444828451
ISBN 13: 9780444828453
Author: Reiner Kuhnau
Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe’s distortion theorem.
There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).
· A collection of independent survey articles in the field of GeometricFunction Theory
· Existence theorems and qualitative properties of conformal and quasiconformal mappings
· A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Table of contents:
Chapter 1. Quasiconformal mappings in Euclidean spaces
Chapter 2. Variational principles in the theory of quasiconformal maps
Chapter 3. The conformal module of quadrilaterals and of rings
Chapter 4. Canonical conformal and quasiconformal mappings. Identities. Kernel functions
Chapter 5. Univalent holomorphic functions with quasiconformal extensions
Chapter 6. Transfinite diameter, Chebyshev constant and capacity
Chapter 7. Some special classes of conformal mappings
Chapter 8. Univalence and zeros of complex polynomials
Chapter 9. Methods for numerical conformal mapping
Chapter 10. Univalent harmonic mappings in the plane
Chapter 11. Quasiconformal extensions and reflections
Chapter 12. Beltrami equation
Chapter 13. The application of conformal maps in electrostatics
Chapter 14. Special functions in Geometric Function Theory
Chapter 15. Extremal functions in Geometric Function Theory. Higher transcendental functions. Inequa
Chapter 16. Eigenvalue problems and conformal mapping
Chapter 17. Foundations of quasiconformal mappings
Chapter 18. Quasiconformal mappings in value-distribution theory
Chapter 19. Bibliography of Geometric Function Theory
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Tags: Reiner Kuhnau, Handbook, Complex, Analysis, Geometric