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Geometric Function Theory in One and Higher Dimensionsby Ian Graham; Gabriela Kohr
Marcel Dekker Inc 2003; US$ 99.95This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions. It introduces the infinite-dimensional theory and provides numerous exercises in each chapter for further study. more...
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Cambridge University Press 2002; US$ 67.00This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and its many applications. It is intended as an accessible resource for engineers, scientists, and applied mathematicians who may not have much prior experience with theoretical or computational conformal mapping techniques. more...
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World Scientific 2004; US$ 107.00The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods. more...
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Elsevier 2004; US$ 275.00Geometric 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... more...
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