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The Beltrami Equation
This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, un...
Moduli in Modern Mapping Theory
Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.
The Confusion between Art and Design
In the past century the borders have blurred between art and design. Designers, artists, aestheticians, curators, art and design critics, historians and students all seem confused about these borders. Figurative painting was reduced to graphic design while still being called 'art'. Figurative sculpture was reduced to nonfunctional industrial design while being called 'sculpture'. This fundamental blunder resulted from total misunderstanding of the concept of "abstraction" by the founders of modern art. Comprehensive analysis shows that so-called "abstract art" is neither abstract nor art, but a very simple, even trivial, kind of design. In this book the prehistoric, philosophical, logical, h...
Mappings with Direct and Inverse Poletsky Inequalities
The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.
Lipa's Legacy
The mathematical works of Lars Ahlfors and Lipman Bers are fundamental and lasting. They have influenced and altered the development of twentieth century mathematics. The personalities of these two scientists helped create a mathematical family and have had a permanent positive effect on a whole generation of mathematicians. Their mathematical heritage continues to lead succeeding generations. In the fall of 1994, one year after Bers' death, some members of this family decided to inaugurate a series of conferences, "The Bers Colloquium", to be held every three years. The theme was to be a topic in the Ahlfors-Bers mathematical tradition, broadly interpreted. Ahlfors died a year after the fir...
Contemporary Controversies in Catholic Bioethics
This volume comprises various viewpoints representing a Catholic perspective on contemporary practices in medicine and biomedical research. The Roman Catholic Church has had a significant impact upon the formulation and application of moral values and principles to a wide range of controversial issues in bioethics. Catholic leaders, theologians, and bioethicists have elucidated and marshaled arguments to support the Church’s definitive positions on several bioethical issues, such as abortion, euthanasia, and reproductive cloning. Not all bioethical issues, however, have been definitively addressed by Catholic authorities, and some Church teachings allow for differing applications in divers...
Handbook of Teichmüller Theory
The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics,...
Harmonic Analysis and Partial Differential Equations
Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
