Complex Analysis: Conformal Inequalities And The Bieberbach Conjecture (monographs And Research Notes In Mathematics)
by Prem K. Kythe /
2015 / English / PDF
3.3 MB Download
Complex Analysis: Conformal Inequalities and the
Bieberbach Conjecture
Complex Analysis: Conformal Inequalities and the
Bieberbach Conjecture discusses the mathematical
analysis created around the Bieberbach conjecture, which is
responsible for the development of many beautiful aspects of
complex analysis, especially in the geometric-function theory of
univalent functions. Assuming basic knowledge of complex analysis
and differential equations, the book is suitable for graduate
students engaged in analytical research on the topics and
researchers working on related areas of complex analysis in one
or more complex variables.
discusses the mathematical
analysis created around the Bieberbach conjecture, which is
responsible for the development of many beautiful aspects of
complex analysis, especially in the geometric-function theory of
univalent functions. Assuming basic knowledge of complex analysis
and differential equations, the book is suitable for graduate
students engaged in analytical research on the topics and
researchers working on related areas of complex analysis in one
or more complex variables.
The author first reviews the theory of analytic functions,
univalent functions, and conformal mapping before covering
various theorems related to the area principle and discussing
Löwner theory. He then presents Schiffer’s variation method, the
bounds for the fourth and higher-order coefficients, various
subclasses of univalent functions, generalized convexity and the
class of
The author first reviews the theory of analytic functions,
univalent functions, and conformal mapping before covering
various theorems related to the area principle and discussing
Löwner theory. He then presents Schiffer’s variation method, the
bounds for the fourth and higher-order coefficients, various
subclasses of univalent functions, generalized convexity and the
class ofα
α-convex functions, and numerical estimates of
the coefficient problem. The book goes on to summarize orthogonal
polynomials, explore the de Branges theorem, and address current
and emerging developments since the de Branges theorem.
-convex functions, and numerical estimates of
the coefficient problem. The book goes on to summarize orthogonal
polynomials, explore the de Branges theorem, and address current
and emerging developments since the de Branges theorem.