Description
Elsevier Handbook Of Complex Analysis Geometric Function Theory by Reiner Kuhnau
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. _x000D__x000D_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 Koebes distortion theorem. _x000D__x000D_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)._x000D_ _x000D_Preface (R. Kuhnau)._x000D_
Quasiconformal mappings in euclidean space (F.W. Gehring)._x000D_
Variational principles in the theory of quasiconformal maps (S.L. Krushkal)._x000D_
The conformal module of quadrilaterals and of rings (R. Kuhnau)._x000D_
Canonical conformal and quasiconformal mappings. Identities. Kernel functions (R. Kuhnau)._x000D_
Univalent holomorphic functions with quasiconform extensions (variational approach) (S.L. Krushkal)._x000D_
Transfinite diameter, Chebyshev constant and capacity (S. Kirsch)._x000D_
Some special classes of conformal mappings (T.J. Suffridge)._x000D_
Univalence and zeros of complex polynomials (G. Schmieder)._x000D_
Methods for numerical conformal mapping (R. Wegmann)._x000D_
Univalent harmonic mappings in the plane (D. Bshouty, W. Hengartner)._x000D_
Quasiconformal extensions and reflections (S.L. Krushkal)._x000D_
Beltrami equation (U. Srebro, E. Yakubov)._x000D_
The applications of conformal maps in electrostatics (R. Kuhnau)._x000D_
Special functions in Geometric Function Theory (S.-L. Qin, M. Vuorinen)._x000D_
Extremal functions in Geometric Function Theory. Special functions. Inequalities (R. Kuhnau)._x000D_
Eigenvalue problems and conformal mapping (B. Dittmar)._x000D_
Foundations of quasiconformal mappings (C.A. Cazacu)._x000D_
Quasiconformal mappings in value-distribution theory (D. Drasin. A.A. Goldberg, P. Poggi-Corradini)._x000D_