Handbook of Complex Analysis: Geometric Function Theory
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Table of contents
- Cover
- Handbook of Complex Analysis: Geometric Function Theoryiii
- Copyright Pageiv
- Contentsxiii
- Prefacev
- List of Contributors of Volume 1vii
- List of Contributorsix
- Contents of Volume 1xi
- Chapter 1. Quasiconformal mappings in Euclidean spaces1
- Chapter 2. Variational principles in the theory of quasiconformal maps31
- Chapter 3. The conformal module of quadrilaterals and of rings99
- Chapter 4. Canonical conformal and quasiconformal mappings. Identities. Kernel functions131
- Chapter 5. Univalent holomorphic functions with quasiconformal extensions165
- Chapter 6. Transfinite diameter, Chebyshev constant and capacity243
- Chapter 7. Some special classes of conformal mappings309
- Chapter 8. Univalence and zeros of complex polynomials339
- Chapter 9. Methods for numerical conformal mapping351
- Chapter 10. Univalent harmonic mappings in the plane479
- Chapter 11. Quasiconformal extensions and reflections507
- Chapter 12. Beltrami equation555
- Chapter 13. The application of conformal maps in electrostatics599
- Chapter 14. Special functions in Geometric Function Theory621
- Chapter 15. Extremal functions in Geometric Function Theory. Higher transcendental functions. Inequa661
- Chapter 16. Eigenvalue problems and conformal mapping669
- Chapter 17. Foundations of quasiconformal mappings687
- Chapter 18. Quasiconformal mappings in value-distribution theory755
- Chapter 19. Bibliography of Geometric Function Theory809
- Author Index829
- Subject Index849
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings.
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).
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).