Geometric function theory
著者
書誌事項
Geometric function theory
（Handbook of complex analysis）
Elsevier, 2002-2005
- v. 1
- v. 2
大学図書館所蔵 件 / 全28件
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v. 1413.5//G35//023415100215167,15100202348,
v. 2413.5//G35//203315100215175,15100220332 -
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注記
Includes bibliographic references and indexes
内容説明・目次
- 巻冊次
-
v. 2 ISBN 9780444515476
内容説明
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).
目次
Preface (R. Kuhnau).
Quasiconformal mappings in euclidean space (F.W. Gehring).
Variational principles in the theory of quasiconformal maps (S.L. Krushkal).
The conformal module of quadrilaterals and of rings (R. Kuhnau).
Canonical conformal and quasiconformal mappings. Identities. Kernel functions (R. Kuhnau).
Univalent holomorphic functions with quasiconform extensions (variational approach) (S.L. Krushkal).
Transfinite diameter, Chebyshev constant and capacity (S. Kirsch).
Some special classes of conformal mappings (T.J. Suffridge).
Univalence and zeros of complex polynomials (G. Schmieder).
Methods for numerical conformal mapping (R. Wegmann).
Univalent harmonic mappings in the plane (D. Bshouty, W. Hengartner).
Quasiconformal extensions and reflections (S.L. Krushkal).
Beltrami equation (U. Srebro, E. Yakubov).
The applications of conformal maps in electrostatics (R. Kuhnau).
Special functions in Geometric Function Theory (S.-L. Qin, M. Vuorinen).
Extremal functions in Geometric Function Theory. Special functions. Inequalities (R. Kuhnau).
Eigenvalue problems and conformal mapping (B. Dittmar).
Foundations of quasiconformal mappings (C.A. Cazacu).
Quasiconformal mappings in value-distribution theory (D. Drasin. A.A. Gol'dberg, P. Poggi-Corradini).
- 巻冊次
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v. 1 ISBN 9780444828453
内容説明
Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers.
目次
Preface.
List of Contributors.
Univalent and multivalent functions (W.K. Hayman).
Conformal maps at the boundary (Ch. Pommerenke).
Extremal quasiconformal mapings of the disk (E. Reich).
Conformal welding (D.H. Hamilton).
Siegel disks and geometric function theory in the work of Yoccoz (D.H. Hamilton).
Sufficient confidents for univalence and quasiconformal extendibility of analytic functions (L.A. Aksent'ev, P.L. Shabalin).
Bounded univalent functions (D.V. Prokhorov).
The *-function in complex analysis (A. Baernstein II).
Logarithmic geometry, exponentiation, and coefficient bounds in the theory of univalent functions and nonoverlapping domains (A.Z. Grinshpan).
Circle packing and discrete analytic function theory (K. Stephenson).
Extreme points and support points (T.H. MacGregory, D.R. Wilken).
The method of the extremal metric (J.A. Jenkins).
Universal Teichmuller space (F.P. Gardiner, W.J. Harvey).
Application of conformal and quasiconformal mappings and their properties in approximation theory (V.V. Andrievskii).
Author Index.
Subject Index.
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